Landing gear is one area (citing your post) is the one area where I'd argue that the P-51H was "weaker" than the earlier models. Obviously, it got the job done, but seeing a P-51H parked it looks spindly compared to how "beefy" the rest of the plane is. Same thing with the lightweights that spawned the H. It always looked weird to me, though I like the H as a flyer because of its performance--basically it was if Ed Schmued could do it over again (WWSD), and many of those design ideas ended up also in the F-82.
Granted, IMO, the P-51H was a "porker" compared to the XP-51F/G, though to be fair, those were proof of concept planes that I don't think were seriously looked at for production. Still, lighter weight, more power for the H made it the premier Mustang. I'd bet that the Germans and Japanese were glad it got ordered and put into production too late to see much use (no combat use as far as is known, only a few issued to squadrons).
That, and the H did deal with the annoying CG/directional stability issues that the rear fuselage tank caused (taller tail--though not on the very first planes--, longer fuselage, smaller tank), though I did see a reference on here that it could've carried a ton more fuel there than the B/D without hurting handling too much.