Why can't you increase the box size?

And with that shallow a box you will probably exceed box fill anyway.

I can't increase it because it's real wood wainscoting panels over a block foundation wall.

"I can't increase it because it's real wood wainscoting panels over a block foundation wall."

Cut a recess into the block.

Now you know why interior walls should be framed out from foundation walls.

I HATE furring strips for this and other reasons.

How about a wall mount remote control and put the dimmer somewhere where it does fit?

Here is a link that might be useful: Pico with wall mount

a single gang wiremold extension of the box will acomodate a dimmer.

Here is a link that might be useful: wiremold device box extension

"a single gang wiremold extension of the box will acomodate a dimmer."

And look hideous in a residence.

Bringing this back up to the top as I think I've found a solution. I found an on-line source for a custom made switch plate cover. I can have it made thicker to accommodate the dimmer. If the box is 1 1/8" deep, how thick will I need to order the plate cover to allow the dimmer switch to fit?

"how thick will I need to order the plate cover to allow the dimmer switch to fit?"

You will have to buy a dimmer and measure.
There is no actual standard for things like this.

You may be over allowed box fill anyway.

You will have at least 1 hot, 1 neutral, a device (the dimmer) that takes 2 allowances, 1 allowance for grounds.

That means you have a fill allowance of at least 5 conductors.
#14s take less volume than #12s.

If you used any internal box clamps they add another allowance.