That is a remodel box. The ears are necessary to hold the box from falling into the wall. You might try digging a shallow groove in the sheet rock where the ears are allowing a slight ingres. Not much, only as deep as the thickness of the ears.

 

Break the plaster ears off of the switches.

 

Ok. I’m a total noob. You means these metal parts?

 

Yes. They add thickness and are not needed then the device strap will go back into the recessed area between the box ears.

 

How is that going to happen? The part of the device with the holes for the mounting screws will still sit on top of the box.

 

Get a "deep" cover plate. They have longer sides.

 

When you unscrew the switch you can see the indentiom of the box that, by removing the ears which extend over the box ears, you can see how it drops back a tiny bit. This is a proper thing to do when you do not need the switch ears to hit the sheet rock to hold it out.
I understand the issue is compounded by the screw less plate you have since they have no forgiveness from the back side.

 

ok ... news flash ... carve this in stone ... I was wrong. I don’t have any experience with old work boxes ... that’s my excuse. :} Looks like there is a shallow recess there.

 

As they say, never too old to learn. That's why they require years of experience working as an electrician before you can get a license.

 

I do the same with devices in a utility box. The cover will fit better there as well.