MDF is going to crumble. Either use hardwood instead or fill the larger engraved areas. (Acrylic paints work well for this. There are some made specifically for this purpose, e.g., from Rowmark, but normal craft store acrylic paints work just fine.)
Unfortunately, the success or failure of a deep engrave is going to be somewhat material dependent - that stuff looks pretty rough. If the glue is inadequate, you might get some flaking on it after the fact.
I see that you’re running tests on it which is great, it’s the only way to lock down the settings that work for any particular material.
What I’d suggest is to keep running engrave tests until you find some settings that do not cut through the veneer. It’s going to look more uniform that way.
The slower speed settings are going to cause charring, and that also causes flaking. What you’ll want to use is 1000 speed for your engraves, and start reducing the power to engrave less deeply. LPI should probably be in the 195-270 range to keep from cutting too deeply.
You can also try full power with a defocused engrave - it will cut much more shallowly. (Add 0.1 inch to whatever the actual thickness of the material is.)
There’s a vinegar / steel wool mixture you can make for aging wood and dying leather – I tried some of it last night on the engraved portion of some PG plywood that I wanted to darken, and it came out a really nice, even dark almost-black color. I’m currently horizontal and drinking coffee to help me recover from a long day of driving all over creation visiting psychiatric clients in adult foster homes, but as soon as I muster the strength to drag myself to my workroom I’ll take a photo of it to post here.
Well, the color didn’t dry quite as even as it looked last night, but it’s definitely nice and dark…this is cherry PG plywood, with the engraved areas lightly cleaned with a stiff brush and then painted with a solution consisting of vinegar with steel wool dissolved in it. I didn’t think to take a before photo to show how much darker it is than it was before, sorry about that. (The answer, though, is “a LOT.”)
I painted it before removing the masking. You can see that in some of the thin areas, the dark color crept in a little, but I think even without masking, in the larger areas the finish would probably prevent it turning the unengraved areas dark. Overall I think it’s a promising technique.