A big part of me thinks that you ended up giving too much to clans which didn't really have a lot of industrial potential. Notably the Blood Spirits, Goliath Scorpions, and Ice Hellions. Now I understand that the Scorpions and Hellions are the ones that kick off the new arms race, but I don't see their 'mechs necessarily always coming out on top, regardless of getting there first.
With the idea that the Ice Hellions and Scorpions are kicking off the arms race, this is kind of how I see the overall industrial potential of most of the clans, at least regarding how much they put to OmniMech production:
Blood Spirits 3 (4)
- they actually get 4 slots due to entirely using standard engines
Burrock 3
Cloud Cobra 2
- very focused on aerospace power so are lower than otherwise expected
Coyote 4
Diamond Shark 4
- likely those designs that are the most ubiquitous among all the clans, not necessarily those produced by the most clans
Fire Mandrill 3
Ghost Bear 5
- fluffed as being able to make what they need when they need it, few if any of their produced designs are likely to be exclusively theirs
Goliath Scorpions 4
- have one larger than likely industrial capability due to getting the jump on other clans
Hell's Horses 3
- focus heavily on combat vehicles, but still have good industrial capabilities
Ice Hellion 3 (4)
- they actually get 4 slots due to their focus on smaller units
Jade Falcon 5
- one of the premier clans, thus first rate 'mech production
Nova Cats 4
Smoke Jaguar 4
- at this point they aren't straining their resources to the breaking point, otherwise they'd probably be at 3
Snow Ravens 3
- focused on warships, but this gives them a larger ability to acquire resources and put them to use than the Cobras
Star Adders 4
- designs are going to be able to fill most, if not all, roles in a touman, likely as generalist as they can get and running the gamut between small recon and large assault 'mechs
Steel Vipers 4
- with control of hellgate they have access to significant resources, after the Battle Cobra and Crossbow, the other two are likely to be higher-end units
Wolf 5
- like the Falcons, one of the premier clans, and having first rate 'mech production
An example would be the Blood Spirits (mostly because they come first alphabetically). Normally they wouldn't have the industrial capability to reliably produce more than a few designs in the numbers they want, but they've taken the drastic step to reduce resource costs significantly in using standard engines. This allows them to have the resources to produce a fourth design for their touman. Their limited contact with the rest of clan society means that their designs are going to need to fulfill most of the needs the touman expects to face.
Design 1: Unnamed 35-tonner 7/11/0 SFE - this design fills the role of recon in force and harrasser
Design 2: Stooping Hawk - High mobility trooper
Design 3: Crossbow - Heavier trooper, design traded from the Snow Ravens who stole it from the Steel Vipers.
Design 4: Blood Spirit - Their iconic 'mech, and heavy assault unit, unfortunately not entirely theirs, having help from either or both the Fire Mandrills (one of the kindraa) and Snow Ravens.
Lastly, I've never liked the "II" designation of some of the later OmniMech designs, rather I'd prefer them to have new names which hearken back to the original. Here are my suggestions for some of what you've proposed:
Mad Dog II -> Rabid Cur
Hellbringer II -> Ragnarok
Grizzly II -> Abyssal Grizzly
Executioner II -> Dullahan
Gargoyle II -> Grotesque (not sure if you were going to go with a new version of this)