A long time ago I got the RCBS collet pullet that screws into the press. Some bullets pulled fine with just slight marks on them.
Others required the collet to be tightened well past "hand tight" mashing and distorting the bullets, and STILL sometimes they slipped out requiring the process to be repeated. Was NEVER able to pull a lead bullet and have it survive. Real pain in the butt.
A few years ago, just for snits and giggles, I bought the Lyman "Orange Hammer" inertia type puller. Works WONDERFULLY!!! Pulls everything, doesn't damage anything!! I pulled 400 7.62NATO without any problems, and without needing to seat the bullets any deeper to break the seal. Most only took 3-4 wacks a few took 6.
Big fan of the hammer over the collet, here!!!
A couple points, never, NEVER, NEVER use the hammer with RIMFIRE ammo!!!!
The other point is you need a hard surface for the hammer to work best. Wood is not hard, and despite how it feels when we fall on it, concrete isn't that hard, either. The hammer doesn't need to be swung hard, it needs to be swung fast, and stop suddenly, for best results. Wood nd concrete slightly cushion, that sudden stop. It will still work, but not as easily.
I found the cast iron top of my COLD wood stove to be ideal. I suppose an old skillet would work just as well.
Forget the press mounted stuff, just use the hammer according to the instructions (DO NOT substitute any components of the hammer!!), and you'll get the job done well, and be totally safe. AND, the bullets can be reused! (Soft lead pointed bullets can have the tips slightly flattened, you can put a small piece of foam or even paper towel in the bottom to prevent this, if needed. Jacketed bullets don't care...)