We got a new laminator recently and if I load it really weird I can get within about 1.5mm tolerances over a whole roll.
It is pretty dumb and probably only works on our model (haven’t tried it with our old one yet). should probably be similar to all your methods but I tape the new roll(s) of lam and vinyl to the actual rollers.
Basically when loading the lam, I just pull enough laminate (including the backing paper, not peeled yet) to tape it to the top roller. I just tape the centre to keep it even.
I then run it through a little so the lam part is going through the rollers. Once that’s running through, I use a safety knife to cut the backing paper of the lam and attach that to its takeup. (Obviously careful not to cut the lam).
once the lam comes out the other end, make sure it’s not taped any more, I usually just poke the tape with a screwdriver.
Then I load the printed roll, do that as normal but instead of taping that to the old piece of backing paper/vinyl/whatever is already in I tape that to the bottom roller.
same again, run it though a little then when it shows at the other side I pick the tape off so it doesn’t wind round the roller.
After that, it’s pretty much good to go. Attach to the takeup and I can run it full speed (10m a minute - 5 mins a roll) with little to no shift.
Only downside to that method is you need to be careful to not let any of the bits taped to the roll to stay that way or your job will run round the roller lol. (Haven’t had that happen yet).
naturally the benefit to that method is the lam doesn’t get stretched at all and doesn’t require any pressure to load. So we don’t get any jobs curling up at all after laminate is applied. Whole process maybe takes about 4 mins to load a new roll and only needs about 300mm of lam every time with the newer laminator. Nice and consistent!