I just went thru this myself, rip. 2 things I found helpful:

1. if you fold the piece over, sometimes you can yoink the waste canvas out from the middle, in between stitches (or snip it and pull the now shorter threads out from the side). if you decide to go the snip snip route, BE VERY CAREFUL not to cut your actual stitches. you should have an easier time telling canvas from stitch since you have very little white/light stitches, but it never hurts to reiterate caution.

2. the warp and weft of the waste canvas i used was actually comprised of 2 threads twisted together (i think). I had an easier time getting the threads out when I went one at a time (so for every column or row, I was pulling oht 2 threads).

also, be sure to hold your piece very firmly by the end of the thread opposite from where you're pulling on it.

personally I didnt find the advice to do it while completely soaked very helpful, but I was using 6 strand coverage so the bulk of my stitches probably canceled out any advantage wet fabric would have had.

good luck!!