So the new update, V1.0.2 seems to have fixed the issues! I've only done one 5 hour flight so far, (much less with X4 time compression :-), but the new update seems more stable and input into the FMS no longer is laggy. I did make a few other changes on my PC, so have listed those below, in case the issue was a combination of things.
Updated to V1.0.2
Cleared the WASM folder
Updated NVIDIA GeForece Game Ready driver to 572.70
Updated DLSS Frame Generation to 310.2.1 (DLSS already at 310.2.1)
Thanks iniBuilds for rolling out these updates quickly!
Update: Just completed a long second flight, this time in the -1000 (first flight was in the -900), ZSPD-EGLL, with no issues. This is the first time I've been able to do a long-haul flight in the A350 without incident, so am really pleased with V1.0.2!