Mounting a mosaic modularly
I can suggest using a base MILS module (BTM-1 on the picture below), basically an extra layer including some Technic Bricks around the edge for connectivity between modules as well as some plates on top of existing baseplate. Yes, it is going to be bulkier and heavier, but at the same time much more sturdy and easy to assemble and take apart for travelling.
This also has an added benefit of making your surface 3D (BTM-2) if needed.

UPDATE
LEGO has now produced their own MILS-like elements used as a base layer for mosaic sets as well - Technic, Brick 16 x 16 x 1 1/3 with Holes (65803)