Rather than use "destroyed" or disbanded divisions as training cadres, these units were probably used to repair combat losses on the fly as Chieftain sustained horrendous losses.
We know Kerensky used the Republic to refit his troops after the Periphery Uprising, but reorganize is probably a better description to describe what occurred. Kerensky also more or less abandoned the Republic during his march to the Hegemony (as the Commonwealth's "invasion" of the Republic illustrates - they simply filled a void left by the departing SLDF troops), so I'm not even sure where your training cadres would have provided training.
With the House Lords supplying little in the way of support, I also highly doubt the SLDF would have been able to utilize the safety of the member-states to host training cadres. So if Kerensky was using disbanded or "destroyed" units to train new replacements these troops would have to cycle at the very minimum, back to the Republic.
Which, as I mentioned earlier seems unlikely due to the actions of the Commonwealth, but also the shear distance between the Hegemony/Republic and the ships required to do so - ships that are desperately needed to prosecute the invasion. These are resources and travel times the SLDF couldn't count on or commit to once Chieftain began. A round trip between the Republic and the front is quite an amount to tack onto even a short training period.
(Transports are also an interesting question since Kerensky is specifically stated as having the SLDF scour/buy all available transports in preparation for the Exodus. At some point during the invasion the SLDF's transports were beginning to dwindle.)
As for the large reserve command, where was the reserve command located, organized and equipped? Answer: the Terran Hegemony.
Amaris's seizure of the Hegemony cut the heart out of the SLDF's logistic network. Loss of the Hegemony would have thrown the entire support apparatus into chaos while shattering its very foundation. Keep in mind, most of the SLDF's major stores and replacements would have been in the Hegemony, and cycled out as needed in a situation reminiscent of the Reunification War.
Remember, the SLDF was designed to fight in a Reunification War-type scenario, with a secure rear area feeding campaigning armies a steady stream of supplies and replacement troops.
While the SLDF did have hundreds, maybe thousands of bases throughout the Inner Sphere they were basically supply waypoints connecting all the way back to the Hegemony. After all, Kerensky stripped every base of consumables on his way to the Republic and then again during the trip back towards to the Hegemony. These consumables were all that remained of a once-powerful support network now dried up.
One hit wonders.
The SLDF had neither the money, nor the manufacturing, training or support structure to replace anything they used until the Hegemony was reconquered.