Very Nice - I like the foam idea. Just as a side note, I used a plate glass as it held under 'downward' pressure and did not move around so much. The glass also helped in putting the plan underneath the glass so that I could glue directly 'to' the glass. However, nothing wrong with your method - it is a good method and I have to remember this one for sure. Thank you for sharing your build.
ps. I am sure with your experience that you are familiar with how laser-cut parts always produce an angle of the part. The effect of this can be observed by the fact that the 'joined' frame parts are 'snug' on one side, while there is a 'gap' on the other side of the part. The problem with sanding or filing those parts down so that 'both' sides are flush is that it WILL affect the overall dimensions of the completed single frame - we all know that errors will accumulate. So, you might want to be watchful to not file too much. I just made sure that one of the sides was joined tightly and did not worry about the gap on the other side.
However, let me say this clearly, you and others might have a different opinion and idea - and that is ok. Just stick with one trajectory and stick with it. I am sure that you will produce a fine model.
Also, I am sure that you are familiar with this, and if you are my apologies in advance, but this is what I used to remove the burned laser char from the parts. I bought a drum sander kit from Harbor Freight and built a level platform so that part will lay on its side flat and ran the part past the sander - However, this method
ONLY is to remove the char - as you know the frames will be
'faired to shape'.