I’ve done this with a Glowforge before to create a lake depth map (similar idea - but reversed). I traced the contours from the map in Inkscape then cut it into baltic birch 3mm or 1/8” plywood from Woodpeckers.
Yes I’m sure it’ll be fine as long as your laser doesn’t have problems with it and it’s very close to 3mm. Kerf isn’t too big a deal with the Birch because it’s softer relative to the mdf so a tight fit isn’t a problem, just a few taps with a mallet and you’re good. Some adjustment to your kerf setting might be necessary with the hardboard, but it’s more than likely to be closer to a true 3mm than the birch and will probably work just fine.
Cut a couple of the smaller pieces that fit into each other before you do the whole thing and make sure you’re happy with the fit so you don’t waste any material.
Alternatively, you can get the Baltic a birch in small sheets from Amazon. Baltic Birch
Or at Woodworker’s Source
I used WWS until I found a good local yard to buy my wood from.
Hope that helps.