I did some testing with what you suggested, and here are the results. I made a rectangle and cut at 5 different focal lengths. The plywood thickness is 3mm. I used honeycomb pin downs, and checked to make sure there was no give in the plywood before I cut it.
The far left were done at 3mm, but double passes (the boxes not labeled).
The ones labeled were single pass cuts in order of thickness in .25 mm increments- 3.5mm, 3.75, 4, 4.25. I ran 170/full for all passes. I honestly can’t tell a difference in any of them. In all cases, the cutting probably went no more than .5mm deep, if that.

I also tried cutting through cardboard, and couldn’t do that either. It went a little deeper but I was worried I was going to catch it on fire if I slowed the laser down anymore.

I can’t imagine I’m doing something so wrong that the laser can’t even cut through cardboard, in this case it’s only 2.8mm thick. I used power 100, and tried speeds of 150 and 125. (The top box was done at 125). It seems like people are doing it on here all the time with ease.
Based on this, does it point to my Glowforge having some kind of focus issue? Will GF only support me on this issue if I use their Proofgrade material? It looks like they shipped out my replacement crumb tray. I just really didn’t want to wait until it gets here, but I’m not sure if they will consider this as a valid test. (I did measure the crumb tray I have, and it’s only the honeycomb that is warped on the far right side- I was able to get the wobble in the tray out by putting some tape over the divet, and checked the level).
Interesting. I found another post, and it looks like this person has a very similar issue, and the resolution was to get a new unit.