I can see this working for pieces that are cut from within the stack like ornaments, but not for portraits. I too do not like blue tape on the bottom of the piece because of the friction and unevenness. What I do is clamp the stack in my bench vise then apply blue tape to just the edge of the stack. If needed, I’ll use an Excato knife to trim the tape.
For stacks other than portraits, I use a hot glue gun to tack the edges only. Years ago, I used double stick tape between layers, but it was very difficult to separate the layers without breaking something.