Consider making the tooling to punch out the disks, and use your big press. 10 tons should be plenty.
The problem with
Greenlee punches is that they keep the
hole nice and clean, but bend up the
disks created in the process. You need the other direction.
To mount on the press ram, all you need is a 1 inch diameter bar. Ideally of something hardened. The bottom surface should be flat, and the edges sharp, as that's what will do the cutting.
the female die to mount on the table is also a hard piece of something, with a 1" hole in it - but the top surface is not flat. (Trying to punch the whole circumference in one shot takes too much force). Instead, it is angled like a V, the depth of the V being about 5-10x the material thickness - maybe 0.100" or so. Deeper cuts better, but deforms the disk more.
The punch coming down hits the upper edges of the die - for example, at 12 and 6 o'clock - to start, and as it moves down, the cutting edge eventually reaches the low point of the V, at 3 and 9 o'clock.
Look at
these to get the idea, but remember, these have the center punch like a V (kinda) and the outer die flat - you want the opposite.
Good luck,
Don