Similar to Peter Cook,s suggestion.
1. make an arbor with a 25mm stub to mount the job. There should be a shoulder on the arbor which will keep the workpiece running true so there is no side to side wobble. The shoulder should be 10mm or so i.e. the o.d. around 45mm. The arbor should be turned in one set up so the shoulder and 25mm stub are true make the stub 0.5 mm shorter than the workpiece say 11.5mm, I would under cut the shoulder so only the outter 5mm supports the workpiece. Tap the the end of the stub 8mm or similar. Make a second ‘washer same dia as the shoulder with the centre hole clearance on your chosen clamping thread. Ideally undercut one side like the shoulder. Set this aside.
2. Find the centre of the the square/ rectangle and centre pop or spot drill it this will help in setting up. Remove any burrs from the edge to aid seating and chuck he square workpiece in the 4 jaw. Use the centre mark to centre the job. Bore the 25mm hole; centre drill then use the largest drill your lathe can safely handle, there is no point in doing excessive step drilling when you will be boring the hole to dia. as this will correct any error from the last drilling op.
3. knock off the corners by whatever method suits but don’t get it hot as the job might distort.
4. Re Chuck the arbor and get it running true on the stub dia. and shoulder face. Mount the job and clamp it up, get it running as true as you can i.e. minimise the side to side wobble.
5. Remove the corners, take it slow and watch out as the corners are near invisible when spinning. I would use an HSS tool as carbide won’t like the interrupted cuts. You can swap to carbide once it’s round if needed.
as for the grub screw it sounds like you are drilling radially, that’s going to be tricky to tap and I am not convinced that is a great method given the ratio of the disc dia. to its thickness.
Hope this helps.
Tony