There really should be no play in the front sprocket once bolted down.
Some 750 drive sprockets have a "dish" to them that indicates orientation front-to-rear. I don't recall the 500 having that. This may be a source of your problems that the sprocket is too close to the motor, and case damage will occur.
The frame tube/engine mounting boss in front is concerning to me. When I install motors, I don't tighten any bolts down until all bolts are fully installed. This helps "center" the motor within the frame. I do tighten the 2 10mm bolts underneath the motor first, then work my way up to the front, then upper rear, and finally lower 12mm (the one that hangs the driver pegs). The rear hangar bolts have spacers that somewhat self correct the center, but the front mounting plates need to be installed, and these pull the front tubes and motor together.
Of course, all this is moot if your frame is actually bent
. I think it very wise to have it professionally inspected before you go further. With a repainted frame, visual evidence of it being bent is much harder to detect.
Regarding your rear sprocket and carrier, do you believe there's damage to them, or do you suspect the drive sprocket is causing the misalignment?
Meanwhile, you can do some checking yourself with the front forks off the bike. Using the string box I described earlier, also install a plumb bob from the steering head (remove the triple tree and steering stem). Suspend a bar across the head, string with bob dropped through. This will enable you to determine whether the neck is straight vertically, and use it as a centerline of the frame for measuring side-to-side distances.
Bike on center stand, and shimmed slightly to insure you have a true parallel sitting compared to the ground. Level the bike front to rear, and side-side with a level and shims.
Once level, a small level to test the exterior of the steering head for plumb, and begin finding the centerline of the bike and stringing to your outside lines with tape dimensions. A bit complicated in words, but it's a DIY technique until you get to the frame shop and deposit cost you a penny.