I thought FM: 3085 and JHS: FR did a decent job of giving some support to the lackluster implementation of the Republic. There's a few issues to separate here though, and adding them all into one does some injustice.
1. The Republic's grabbing of a number of those worlds (not all, but a fair amount) is weak.
This is true. As MadCap has discussed elsewhere, Wizkids implementation of the Republic was terrible in the early stages. That's an out-of-universe impact on an in-universe faction. Let's not confuse the two. The two books I mentioned above help to add some support to why particular factions (the former FedCom nations in particular) gave up those worlds. But most importantly, CGL added in things to make it fit more in tone with the individual factions. The Combine played politics and still pulled a fast one on the Republic. "Sure you can have some of our factory worlds. Oh yeah, we moved all the factories and left you the charred rubble. Enjoy." That fits in the tone of the Combine. The Lyrans? "You want to get rid of Skye for us, but we still keep most of the decent factory worlds that haven't been completely reduced to rubble like New Earth? Uhh...where do we sign?" Again, it's a merchants dream. They reduce reconstruction costs, all with what they believe is the very strong possibility that they can come back in the near future to get those worlds back. And really, the Republic gets a bunch of junk worlds with mostly destroyed (or totally destroyed) factories.
So, those things (and more) help to bring the initial poor implementation into line with existing BT material. Is it perfect? Absolutely not. Is it the best of a bad idea that CGL has to live with? Yup.
2. Number 1 doesn't have any impact on the Republic as a faction and whether it fits the aesthetic. The Republic fits the BT aesthetic pretty well in fact, when examined a bit more closely.
The Republic fits in perfectly with the rest of the Successor States, particularly the former FedCom states and the Clans. They claim a great many things about building up their people, strong opportunities for all, etc. Just like every other House...they're as two-faced and full of shit as the rest of them. Every single faction in BT is this way at one point or another. Every last one. It's one of the things that makes it fantastic. They have great thoughts on how to move forward with the Republic and then make the same mistakes that every other faction has made. They left the nobility empowered and entrenched. They want to have things appear to be more above board and public, but continue building up some exceptionally nasty black ops and off the books operators (the Fidelis, using old Blakist wargame scenarios, the Ghost Knights, etc). They talk about equal representation, then give the Exarch the ability to unilaterally disband the only group that is publicly nominated (the Senate). They're just as grimy and grey (with certain specific streaks of pure lily whiteness and evil black-hat in the same kind of proportions) as the rest of the factions.
3. The Republic was never going to be a reborn Hegemony. A reborn Hegemony was never going to be anything resembling the Terran Hegemony, no matter who did it at this stage of the game.
The Hegemony is too long relegated to myth and history to be relevant. No matter what formed on Terra (Blakist, Republic, or otherwise), in the canon material...it wasn't going to look anything like the Terran Hegemony. Not even a little bit. They kept portions of its mystique are still around (the overarching plans and social engineering, ala the moving the various nationalities around in resettlement programs, the technology focus on staying on top, the Cameron-esque cult of personality regarding Stone, and the really scary black bag operators). You just need to look close.
4. The Jihad really was so scarring. Just not quite in the way you're thinking.
One of the things that ER: 2750 has really driven home for me is the massive differences between post-Hegemony Inner Sphere and pre-Fall Inner Sphere. It's not just a matter of the Hegemony that changed. EVERYBODY changed. From the House Lords down to the littlest peon. The entire population of the IS (and Periphery) had a monumentally different sense of scale in the Star League era. The existence of the DoME is proof of that. Not a single faction has since come close to what DoME accomplished, in all the intervening years. Not only have they not come close...they haven't even tried. The further out you get from the League and the Hegemony, the more the people simply look at it as some sort of creation myth or legendary part of mythology. They don't even perceive the worlds around them and the possibilities of what you can do with the same sense of scale that the Camerons and their people did.
The same is true for the Succession Wars. The people living through the Jihad (even the older characters who die off) by and large have not seen the Succession Wars. Not the destructive ones that we're really talking about here (the 1st and 2nd). Those things are ancient history, taking on the mythological sense much like the Hegemony mentioned above. Everybody can read about it, and grasp the impact of what happened...but they cannot personalize it. They cannot conceptualize it with emotional impact at a personal level. It didn't happen to them. We see the same thing in the real world today. We don't doubt the damage or horror of either of the World Wars, but most of us look at more modern events for a sense of emotional horror and loss. It's human nature. The Jihad was that modern event that left personal emotional scarring for a lot of people. Those worlds that remind them of that emotional scarring, those worlds that are going to require massive amounts of funds and reconstruction, the ones that sided with those bastard Blakists (even if they didn't)...somebody wants to take them off our hands so that we can rebuild the "important" worlds in our interior? Fine. Fuck 'em.
It's not about trying to show the Jihad as anywhere near as destructive as the 1st or 2nd SW. I mean, c'mon, the 1st and 2nd manage to kill off at least 750 worlds permanently. The Jihad managed maybe a dozen, two, at best? But what the Jihad did offer is what the 4th Succession War offered to the Capellans. Were the Capellans actually destroyed? Nope. Did the people believe in emotional loss far beyond the actual loss of systems? Did they despair? For a time, yes. And that's the key thing. The Successor States in the early 3080's, when the Republic idea begins to take hold...they're stuck in despair. They haven't processed and dealt with the emotional blow yet, when Stone and Lear come calling with their plans. They're not thinking clearly (and the few that do like the Capellans and the Combine, clearly make out better) and they react emotionally. Again, is it a perfect storyline? Nope. Has CGL done a good job at turning really poorly planned implementation into something that has some legs? Yup.
Just as the Successor States are not the Successor States of the Star League era during the 3025 era (they don't think on the same scale, as discussed above), the Successor States of the Jihad are not the Successor States of the 1st and 2nd Succession War. The 3025 states had no emotional connection to the Star League's ambition and drastic overreach. The Jihad states have no emotional connection to the horrors and destruction of the 1st and 2nd SW. Both of them (the 3025 states and the Jihad states) haven't lived through their respective prior eras to have that emotional connection. They can intellectualize it, they can debate it, they can comprehend it. But they cannot feel it.
Side note: That emotional impact the Jihad brings to the table? Something that has been sadly lacking in BT material to date. I'm not saying material didn't have an emotional impact previous to this. But the idea of showing the citizenry shell-shocked (outside of the SWs) and the very factions themselves having emotional exhaustion...that's one of its strengths. It's something that they missed opportunities on with the Clan Invasion and the FedCom Civil War in particular. They tried to personalize it to specific characters, rather than giving the broader view of humanity.
5. Oh, the Republic pain. I'm a Republic fan, no denying that. (Strangely, I'm also a Capellan fan.) I for one cannot wait for the pain. It's going to be glorious.
I think this is the last I have to say on this for a while, as I've been harping on this elsewhere. Reading the DA PDFs (and there is a wealth of material there, several hundred pages worth) available on the BT site were a bit eye-opening for me. When you start to look between the lines, the Republic offers up the same opportunities that the other factions have. It fits well in the mold of the Hegemony without trying to copy the Hegemony. The core concept holds up strong, while they have worked hard to de-emphasize the really poor introduction of the faction. But I found myself really disliking things about that introduction and the faction that came from me not having information on the Republic. Take a read through those Dark Age PDFs, while reading FM: 3085 and Jihad: FR. Look close. You might be surprised by what you think after that. You may not as well. This is just one fan offering up some food for thought.