You can soak the tape a little bit with water if needed, this can help getting it off easily - I don't know what tape exactly you have by hand, so perhaps you can try before with a piece on your own back of hand, wet it and see how this works in your case?
To me it sounds that either your baby somehow got his foot back in the curled position into the shoe or that she/he just needs some more time.
If the first would be the case -
do you have somebody to help you with putting on the shoe? I know it is not easy to do it alone.
Please apologize if I'm telling now only things you are already doing/got told already

- Unfortunately I didn't have the right material to fasten the stabilizing little cardboard piece enough and as a result couldn't prevent James from escaping the shoe, so after many, many tries I ended up placing a piece of tape with the sticky side upside on a table, then made James stand with his foot spread out on it, placing gently one after one all of his toes like they would be positioned normally (at this point it was helpful that he stood on slightly sticky material, and, that I could compare with his normal foot how everything should look ), then placing a second piece sticky side down over it and pressing all the sticky parts gently together like a sandwich. One can carefully trim the edges of the 'sandwich', I had light yellow tape and in good light I could see exactly where his toenails ended.
That you got a paper/cardboard stabilizator kept in place is great! Best wishes for your little sweetie