Perhaps the solution then is to set different goals for each unit.
Honestly, I see the Remnant as 'Stand and Deliver' using heavies and assaults moving 4/6. It lets them bring the firepower and armor to stand up to Crusader Wolf attacks even if they are slower- and since they would most likely be on the defensive they will not be getting in cavalry skirmishes. Which is not to say they would not have some fast/jumpy lights or mediums on hand, it is just they need to hold the line. I would expect lots of heavy tracked armor with long to mid range firepower, again to hold the line. Light mech roles such as scouting, recon and observation would better be handled by infantry, BA, light vehicles and VTOLs which are not as limited when the Remnant is in a defensive role.
The Fortress Republic however should be more of a cavalry force. They are not going to be out in massive force against the rest of the IS, so being able to get in and get out are more critical. They can dodge heavier forces they may not be able to outgun and thus run strategic circles around defenders as they strike targets. I would say this would be more exhibited on the Crusader Wolf and Capellan fronts as I feel the cavalry tactics and commanders who excel at them should be on those fronts. Slower forces should be adequate for the Dracs, FedSuns (if being struck at all due to Alliance), reformed League, Falcons, Bears and perhaps Lyrans. This formation IMO would have crack mobile BA units assigned, perhaps specially trained (and thus fluffed) for seizing/clearing buildings and perhaps field expedient demolitions. It all depends on what you think the Fortress forces have been doing on the raids.
With that said, I would not mind seeming some Fortress vs Liao combats . . . the RAF on that border seem to have a very large hate on and it would be interesting to see whose equipment lets it play hide & seek better.