Your issues (as far as cutting and construction go) will like be that 60-degree finger joints will have overlaps and gaps that require finishing. if the box is small enough (a few inches per side) it might make sense to build a jig to make real angled cuts. (I doubt you could do a clean enough job with 3D engrave.)
if you want that inside lip, it will be easier with two 1/8 pieces. or a 1/4 outside and 1/8 inside. i’ve done that with rectangular boxes, but not with non-90 deg angled sides. it will be a nice box, but you’ll find non-90 deg angles to be more complicated to deal with on the laser.
There have been a bunch of discussions of angled cuts, but (essentially) the idea is to take out the crumb tray and put in a slanted support that will hold your piece at the angle you want to cut. The piece you’re cutting can only be so long because one end will be on the floor of the GF and the other end will be up in the air above where the crumb tray used to be, and you can only really cut straight lines in particular places where the surface of the piece is within focusing range. For Hex you’re talking 30 degrees, and the highest you can focus is about 1.9" off the floor, so your max length would be about 3.8"
Oh, and the GF bottom is also magnetic, so you can hold your jig down with magnets.
I think you’re going to have to do the angled cuts once the pieces are near final length. You will likely need to experiment with focus because different parts of the cut will be at different heights. Maybe separate into multiple jobs by using colors…