Advice needed on my Craftsman 315-series Table Saw

My 315-series cannot hold a bevel set. I use an Angle Cube to set a bevel, say, 11.25 degrees, which I must hit dead-on (I’m making stave drums with 16 staves, and with a total of 32 bevels a .01 error adds up to open joints when gluing up the circle). It is incredibly finicky to get to that setting, and when I do finally hit it, it may move while I’m tightening the bevel lock, or even just setting a piece of wood on the saw. I’ve examined, cleaned, lubed, etc., everything I can think of, and my current conclusion is that the tilt screw mechanism has just enough slop in it to be the source. In looking for parts, I’ve found lots of 113-series tilt screw parts on eBay, but nothing for the 315. Any thoughts or advice, short of buying a new saw (I am investigating that but choking on the cost!) would be most kindly appreciated.