It has been close to two decades since Dale Fritts made and showed me his collet holder, which accommodated swapping through a decent range of punch diameters (nice feature for core-seating) using gauge pins instead to 'headed' punches, for bullet making. I cannot recall, but believe that [radial] 'floating'
was part of Dale's concept: from my perspective, radial 'float' was/is certainly important - aiding/maintaining concentricity., therefore, that was part and parcel to our effort.
Thus, we began with a simple total float of 0.005" ( radially, a mere 0.0025"), which I considered too 'tight', but a hole can always be made larger . . . in my shop, "putting material back" has proven difficult.

We wound up boring for 0.010" total, or, 0.005" of radial movement: we were stymied at every installation - the punch simply was, "not even close" to entering the die-cavity!
Al will verify that we had assured both the external ram adaptor, and internal bore indicated to within 0.0002" concentricity AND were parallel, with a nicely perpendicular shoulder/stop: the collet holder would simply, 'drop into' the adaptor bore, and the punch SHOULD have been almost perfectly aligned - maybe, just wanting a slight radial shift . . . We checked and re-checked the numbers - practically wore out a Mitutoyo dial-indicator!
Mind-bogglingly, every installation resulted in "failure" - then, Al and BIG MIKE held council: what if the alignment iss use was, as it appeared, AXIAL?!!? So much so, that the 'float' notonly fell short, but trying get insert an off axis/angled pin into a fixed bore just won''t work!
So, back to the lathe: to assure concentricity, the supplied collet-holder body and the tapered collet-bore, were indicated as being very close (
<0.002" - likely, as close as my machine, devices and ability will measure) . . . then, the gauge pin was inserted and the closer-nut secured. The axial misalignment was HUGE - how could/can THAT be?!!? The alignment checked and re-checked - it was always lacking.
Finally, we all agreed to install the parts, with the collet nut loose, and the pin inserted into the die cavity and held by hand, raise the ram into position, then snug the collet nut - NIRVANA and repeatable at that! Perfect actuation every test stroke. So, Al decided to head back to uncivilized SD, while BIG MIKE and I cellebrated.
Much remains to explore, including a FULL re-doo, using new/replacement parts, in hopes that this particular collet holder had a misalignment issue which we were unable to identify. Of note, I was pleased that often, AL and I would, simultaneously, "jump to the same [useful] conclusion" - good for my ego, possibly discouraging for AL.
For what appeared a simple project, many doors were left unopened for further exploration. AL can fill in more interesting details and correct my errors . . . we did develop some new concepts, and maybe learned/re-learned some issues involving core-seating and it's relationship to the point-up die, & the finished bullet(s).

RG