I just had 16 gauge wire and found these connections very frustrating. As you note there's no way that 1/4" would hold. I ending up drilling away some of the plastic "above" the pinch terminal so that I could strip about 1/2" of copper and have enough for the terminal plate to grip. Used a 1/8" drill bit and actually inserted it up through the terminal where the wire fits, and drilled up about another 1/4".
This on version 3 QS4s and M3 on-walls.

I also rounded the hex recess on several of the screws, so I used a Dremel cutting wheel to make a slot for a straight screwdriver. Might be quicker and easier than getting a new bracket.