There are alot of threads on the forum with problems doing totes, even with heat presses.... from what I've read, they hold an incredible amount of moisture. Also, some totes aren't good for this process, so it may also be the tote itself.
I know Topper 806 totes have been recommended, and you also need to use totes without sizing on them. I've seen folks use Ironall with totes, so it's probably not the Ironall.
I think to remove the moisture properly, you'll need to insert a towel inside the tote and apply alot of heat. When I removed the moisture from sweatshirts, where there was no towel on the counter, I had to wipe the counter dry, and totes have more moisture than that. (I used to hand iron Ironall.)
With a press, people reverse the tote so the handles hang off the edge and don't melt (others have done that, too.)
Definitely using a mouse pad, or uncorrogated cardboard is a must to raise the imprint area above the seams, even with a hand iron, since you need to apply huge amounts of pressure to the edges of the transfer, and being raised helps alot. A pillow may be hard to use with an iron tho.
Diane/Shuffy does alot of totes and she removes moisture twice (I think it is Diane, be could be Jberte....). All of that info is in the threads, if you search "tote bags" you'll find the threads.