very good explanation of the quantum immortality argument!The reason it doesn't work with a paintball is that the argument for quantum immortality specifically depends on philosophical assumptions about your subjective probabilities of experiencing one branch vs. another ....
However, consider the following. Similar to the Star Trek machine, some copies are made, but this time, "the original" is kept. You're put to sleep before the copying procedure is started, and "the original" and the "copies" are then mixed in a kind of big black box mixer, which has several outlets. Each "copy" together with the original is now presented randomly to an outlet, and waken up. From the outside, there's no way to distinguish the "copies" from the original, and all are on the same footing. But of course, you are still "yourself"! There will be strictly no way, however, to tell the outside world that you are the "original".
Behind one outlet, the head is chopped off, and behind the others, life goes on.
Well, if you happen to be behind an outlet where the head is chopped off, you'll die, and your copies will live on, while if it is a copy who's head is chopped off, you'll live on. There's no way you could "live on" just because there's a copy of you surviving.
So you can consider the star trek machine also as the "murder of the original" together with the re-assembly of copies.
Point is: there is strictly no way to find this out on the outside...