Can a thicker chain cause it to slide/jump under pressure?
No. Most common chains are 1\8 (single speeds) and 2/32 for your average multispeed chain. Of course 8 and 9 speed chains can be thinner.  It may be your sprocket. You didn't state how many miles is on the bike in it's current setup. If the rear sprocket is worn, chain will skip.

Also if the chain alignment is too far off, it will skip or come off. A single speed set up puts more load on a chain without a derailleur to dampen some of it and hold it in place.

A bent chainring on a crank can possibly throw it off or cause similar problems.

If you just shortened your chain and pieced it back together by driving the pin back between the links versus using a or the masterlink, that point can be too tight and inflexable depending on how far the pin was pushed in. It can be microns of a difference and that link won't flex.