EVA has provided good adhesion to laminate desk material when weighed down.  A big sheet can be weighed down by the keyboard.  The problem is its static cling attracts dirt, but the dirt seems to be shaken off more easily than neoprene.  It needs a fabric mouse pad on top to provide the right friction.  

The ultimate mouse pad is trending toward a 12x18" sheet of 1/4" EVA, completely covered in mouse fabric, going under the keyboard.  That's the largest sheet sold locally.  The trick is adhering the fabric to it.

The trick seems to be 1st ironing on adhesive to the EVA, then ironing on the fabric, then cutting the fabric.

A more manly way of doing it is with spray adhesive, a table saw, & a dog.

There are commercially produced mouse pads which cover the entire desk, but they range from 1mm thick to 3mm thick.  They seem to be made of neoprene, with all the problems.  They can be super expensive depending on thickness.

https://www.amazon.com/cimetech-Comfortable-Superfine-Waterproof-645x315x1mm/dp/B07ZNV9B8Z

https://www.amazon.com/dp/B08V8BNPR6/ref=sspa_dk_detail_2?pd_rd_i=B08V8BNPR6

1 advantage of 12"x18" is it's easy to remove for eating & cleaning.  Anything hot is going to warp the EVA.  That makes lions doubtful about ironing adhesive on to EVA.  Elbows compress the EVA, making 1/4" a better thickness.

Caveat lion: EVA shrinks when it gets hot.  It's not clear how anyone is ironing adhesive onto it without warping it.  

After several weeks, the lion kingdom's pad was a warped mess from cookware getting on it.  It might require a commercial mouse pad on temporary EVA.  Note, hacking the mouse cable is the single greatest improvement in mouse mobility.  It should come out of the side at a right angle.  Unlike a wireless mouse, it doesn't die every few days.

If Steve Jobless was still alive, all mice would look like this.