Different firmware is not going to solve the underlying problem of the fan pins being ground-side switching. A number of people on the forum successfully use Marlin with laser support enabled. It is what I use. I’ve never seen a head-to-head comparison of different laser firmware on similar boards, so it is hard to say what impact the firmware plays in the quality of the laser engraving and cutting.
From what I can tell, your board doesn’t break out any extra pins. I found a possible schematic in this forum post. If you want to use this board, I think figuring out how to use a 12V PWM pin is the path of least resistance.
Looking at the schematic, I find four 12V PWM pins that could be used to drive the laser.
Fan - 16, PH4, [7] Hotbed - 1, PG5, [4] Extruder1 - 6, PE4, [2] Extruder2 - 7, PE4, [3]
You can assign a fan pin as the laser pin as used by the laser support in Marlin, but you will need some additional circuitry to address the ground-side-switching issue. I believe I’ve seen a few circuits in posts on this forum to address the issue including Mike’s one above.
Edit: After finishing the above, I did a bit of searching on the forum to see if I could find any of the other circuits diagrams. I found this post, which Mike (@dart1280) also posted. Maybe he can compare and contrast the two circuits. I know I’ve seen a couple of other solutions as well, but they did not show up in my searching.