No flanges on the Y-axis pulley could cause problems, but I guess if the belt doesn't fall of then nothing to worry about. Why have you extended the motor shaft then put a pulley on the end? It seems an expensive way to do it. Surely the motor bearings are sufficient to take the belt tension, or was there another reason? The reason I mention it is you've now added the moment of inertia of that shaft to the system which will affect your acceleration a little.

Which motors are those? I'll be interested to see what feedrate you can get on the X-axis, and whether it's limited by screw whip or motor torque. I'd have been inclined to get 10mm pitch screws. With 20x5mm over that length you're limited to roughly 5000mm/min in theory. Twice that feedrate but less resolution (depending on pulleys) with 10mm pitch screws. Bit late now I guess.

What size is the box section you've used for the frame?

Looks like you're not far off running it now