Many years ago I worked for a biological supply company, making slides for
sale to educational institutions.  I used two products for the mounting of
whole small invertebrates like planaria, daphnia, hydra, mites, etc.
Depending on the dimensions of your "very thick specimens", one of these
might be useful.

The first is depression slides, also called concavity slides.  These are
glass slides, a little thicker than normal, with a round concavity about a
half inch wide and a millimeter deep in the center of the slide. You
slightly overfill the concavity with mounting medium, place the stained,
dehydrated, cleared specimen into the medium, and apply a coverslip larger
than the concavity. The medium flows out to the edges of the coverslip, and
the slide looks just like a typical coverslipped slide, since the edges of
the coverslip lie flat against the slide.

The other method employed solvent resistant plastic rings which came in
various diameters and depths. I used these primarily for mounting larger
specimens like fleas, mosquitos, drosophila, etc. The round rings were flat
on the edges and the top and bottom surfaces, in other words the cross
section of one side of the ring would be square.  I would prepare slides in
advance by dipping a ring into diluted mounting medium or diluted polyvinyl
acetate, placing it on a standard slide, and allowing it to dry, cementing
the ring to the slide. Then the ring could be filled with mounting medium, a
specimen placed into the mounting medium, and a round coverslip the same
diameter as the ring placed on top.

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