I’m curious if a laser isn’t the best tool for this in that case. Have you looked at using a drag knife to accomplish this? You wouldn’t need to deal with the melting or overburning.
Alternatively, have you explored using Dot Mode for this? Not sure it would necessarily help but it might. This would get you very precise power level throughout the entire path. You mentioned the material is very expensive so might be worth experimenting on some scrap material.