I did some more experimenting today, using an alternative to Precision Board called SignFoam. I’m trying to get proper samples to play with, but I’ve been sent 3 artsy samples like this.

These are 3/8" thick, CNC routed. Notice how fine their engraving is, at least as thin as 1/32.
The reason I’m interested is that this is more easily gotten for me, with free shipping (from Harbor Sales). They don’t like to deliver to residences, so I might have to meet the driver in some parking lot. But that’s a lot better than the high costs I was quoted for PB (139 per 4x8 sheet, 1/2", 15 lb; plus $259 shipping, plus tax). Harbor sales price for same in Signfoam: $129 per sheet, free delivery, no sales tax.
I decided to use these small SF samples for some testing today. I wanted to check the flame-retardancy (they claim self-extinguishing), and see how it took to engraving bricks & grain. Also nozzle distances, and more on the effects of speed and power settings, like Dennis suggested.

It seems to do just as well as Precision Board, with one difference: there wasn’t that surface layer that was hard to break through (but maybe that was an older PB sample, who knows).
My fave was this one, ran with a 1/2" gap from nozzle to material.

Of course, the effects can be easily lessened (this grain is too deep). But the mortar lines are really crisp, 1/32 wide and and 1/32 (lower far corner) to 1/16 (upper far corner) deep.
I’m relieved it didn’t want to cat fire (I really tried to light it, but it wouldn’t take). So Signfoam and Precision Board seem to be safe in this regard. BUT, other brands of HDU board WILL torch right up. I tried this with Corafoam and Jasper. Those cannot be used with lasers; but they’re cheaper though, and can be routed and used outside.