It is important to understand how this assembly works. The swing arm bolt, along with the two steel bushings and center spacer, become a structural frame component when installed. Those parts get clamped fair down between the two sides of the frame, and the swingarm and its soft bushings (the factory ones are plastic) spin on this fixed assembly. Radial play is controlled by the bore of the soft bushings, and axial play is controlled by shimming between the frame and swingarm. Actually, on a TX500, the shims are located between the dust covers and the ends of the soft bushings. Likely you have not removed enough material from the frame to be of concern, but you want to file the area flat and perpendicular to the axle. If the face is angled, there will be excess pressure on one spot and axial play will wear prematurely. The missing material on the frame has no effect on the axial play itself, but if the face is not perpendicular, it will wear only in one spot instead of the entire face. You would have to remove a pretty good bit of material from the frame before it becomes a problem requiring a spacer to fill the gap. The axial play is determined by the difference in span of the stack of the two steel bushings and center spacer, and the stack of the two soft bushings and swingarm. When you assemble everything, you will simply tighten the bolt until the frame sides get pulled in tight to the center spacer/steel bushing stack. This will pull the frame sides together slightly more than before but very likely it will make no difference. Most Yamaha engines of that period are mounted to a horizontal cross member, so the engine installation will not interact with the swing arm installation.
File the area flat and perpendicular, and trial fit the dust covers, shims, steel bushings and center spacer into the frame without the swingarm. Without tightening the pivot bolt, look and see how much axial (side to side) play there is between the two sides of the frame. This is how much you will be moving the frame when you tighten it down. If you can tighten it down tight reasonable easily (tight is clamping the parts very tightly between the frame sides, not how hard it is to turn the nut) you should be fine. If it is a big gap, get a ground spacer/shim from a bearing house, or find a really close washer. It's ok to be bending the frame sides in slightly when you tighten the bolt. Just remember, the bolt is intended to be completely tight. It is not any sort of adjustment for the swing arm axial play.
Once you get that sorted out, assemble it again with the swingarm included. It needs to be operating room clean and lubed with some very light oil. Properly assembled and shimmed, there should be ZERO discernible play either radially or axially. If there is axial play, add shims. You can get them from a bearing supply. Likely there are some already inside the dust caps. They are razor thin and usually overlooked by a lot of people - usually glued in with old grease pretty good and easily mistaken for part of the cap. If there are none and you need some, get them from a bearing supply. They should fit pretty closely inside the cap, but have an inside diameter larger than the OD of the steel inner bushings. When you get zero play, take it apart and re assemble everything with wheel bearing grease. It should be quite tight - enough that the arm barely falls from its own weight when held horizontal. Don't worry - it will get a lot freer once you start riding.