Hi Boyan
First of all, you might be a bit too cautious in your approach. The wrap below was one of 72 for a run of 288 mugs, so this wrap was used between 4 and 5 times. As you can see there is excess ink left on the wrap.
However I would have no hesitation in using this wrap as it is for a completely different image.
I have used various types of paper, including standard copier paper once, and would not get "bleed" from a previous print.
It could be that you are concerned about nothing, or it might be worth turning the temp on your oven down a notch or two.
Although I think the paper I use is pretty darn good, the papers you mentioned should also give you stunning results.
And if anyone wants to play along... I will add reputation points to whoever guesses the person... :-)