You might want to try dropping the Y belts completely and then checking to see if the gantry rides ‘square’ in the machine. If you’ve determined the Y axes are sufficiently close to square, then you’re looking for the X to be normal to those. I had to shim the ends of my X rail to get the plates square enough to not tend to pull the gantry out of alignment.
That being said, once the machine is powered up, there’s more than enough holding force in the steppers to pull one end of of the X axis a few mm back into square, more than enough to correct your < 1mm offset.
Whatever you do, you may well find that pushing the machine to the back (or front as others do) in Y against the end plates or against some set-screws to give adjustment is the more reliable way of starting up square.
Of course, starting up square doesn’t help unless the Y belt tensions match and both belts are in decent condition.
I found that measuring the belt tension by tone was the most consistent and effective method, the big upside is that on the two Y axes you can put both belts on blocks and just listen to the tone difference between them to get them even.
I see above you mention a bent stepper shaft, as you say, nothing’s going to work properly until that’s fixed, it makes the rotation eccentric and therefore the distance per step vary.
As I’m stingy, I use four small offcuts of wood in the corners of the machine, simply to maximise the distance over which I’m measuring square to increase the signal to measurement noise ratio a little.