I use the non-slip fabric also. Wrap some around the barrel and hand hold. Put the correct size punch in and tap. Don't try to get it out in a few big whacks. Tap, tap, tap and notice the progress. I often have to re-grip 4 or 5 or 6 times or more. Use patience and expect 3 - 5 minutes or so of tapping. If it comes out in only 1 minute, then great. The point is try and make small progress over several minutes and most of the time the parts will be totally useable again.
In all honesty, I guess I have taken dozens of pens apart, mostly to refinish a blank, and I have never ruined a part.
Each pen type is different. On slim lines, I use a small diameter punch to slide through the transmission and force out the nib, then use a larger punch from the nib end to force the transmission back. On some pens, the nib or clip end must be forced out first and then from the clip or nib end, go in with a large punch and force the inside part out in the other direction.