Aha,
Diagnostics are pointing us toward possible culprits.
So, if the machine is square when all the way forward but when you jog it to the back it is no longer square, that suggests that the two Y belts have unequal tension, see this post for more info. The belts tension by being stretched so unequal tension would mean unequal steps / mm which would mean the machine could only be square at one Y position.
I’d suggest checking the tension of both Y belts, if they’re the same and you still have the problem, it may be that one is starting to fail, replace both if so.
After cutting, filing and shimming the ends of my X beam straight I found that there is more than enough slack in the V wheels to start up off square, I always gently push my X beam into the rear stops before powering up (on my machine this does not over-compress the homing switch) which gives me a consistent X-Y angle and consistent positioning. I still have a repeatability problem on one of the homing switches and as soon as there is stock at Robotshop I’ll try the inductive ones instead.