I know that's cheating but maybe "Realignment IRUs Immediately" works?
It sounds like that might happen in the real world as well. My wild guess is that one way (in the real world) would be to tow/taxi the plane to an area that's better protected from winds (e.g. into a hangar, maybe a runup area with blast shields would also be sufficient?). I've never tried if X-Plane simulates objects shielding from wind though (and it might just not do it, it's usually not important to simulate that), so maybe the "cheat" is the only option.
As an afterthought... If X-Plane does not simulate wind shielding inside hangars etc. we can still control the winds within the simulation. So to simulate shielding from strong winds e.g. inside a hangar it would be possible to temporarily override the winds to be calm in ASXP and restore live weather after the alignment has finished.