Thanks for your reply Tami. I intended to put this on hardi-board from the beginning then attach it to the wall, so I so have a board. The not so sticky contact paper I used was 'removable' contact paper from Home Depot and it really didn't seem very sticky. I found 'permanent' laminate contact paper at Staples (was told this was very sticky - 'not removable') to use over the top of the mosaic, but it's really hard to tell which is stickier!
The height of the stone tile pieces and the glass is about the same, so I don't think that is what is causing my problem. After posting this I tried another test using white glue and paper over the top. Let it dry overnight, and all but one tile stuck to the paper with glue when I pulled off the removable contact paper. (I also read you can use wall paper paste).
I have some mastic that is very thick and doesn't run which I could use instead of thinset, but my mosaic has tiny pieces that, if the mastic is troweled on, may land in the groves instead of the mastic. Unless I just skim on the mastic without groves... but will it dry that way? Not sure.
This has really taught me to test out new ways of doing things before putting weeks into creating a piece. I can just see myself moving my mosaic from the contact paper piece by piece with tweezers to the hardi-board
I haven't seen the double sided adhesive sheet you mentioned, but I'll look for it before I attempt another one.
Thanks for your input