It turned out the that tool I was using was poorly machined, which made me believe the screw heads were to blame. I bought a good quality Torx driver and the screws come out perfectly.
Since I started using my Kangxin again on a regular basis, the 510 wobble had gotten worse to the point where it felt ike catastrophic failure was immanent. Replacing with an FDV shorty realistically felt beyond my skills so I went for another solution.
I wrapped a collar of Unibond epoxy putty around the underside on the 510 and molded into place. After I took the picture below I had to do some very quick scraping and shaping before it cured completely as I had not allowed for a gap around the edge where the main chassis meets the top plate, and some additional clearance for the sled that holds the LCD.
It's reassembled now and it's rock solid with no play at all.
During the repair it became really clear that using a press fitted and glued 510 was a really poor design choice by the engineers who made this otherwise superb
device.