Okay, went to Home Depot and bought half-a-dozen 1/4" x 4" x 4’ “craft” boards (which are actually 1/4" x 3.5" x 4’):
- Poplar: https://www.homedepot.com/p/Weaber-1-4-in-x-4-in-x-4-ft-S4S-Poplar-Board-27404/207058971
- Red Oak: https://www.homedepot.com/p/Weaber-1-4-in-x-4-in-x-4-ft-S4S-Oak-Board-27412/207058962
(and yes, I went through all of the over 200 boards which were in stock at my local store to find the 6 which were decently straight and left the stacks neater than they were when I arrived)
It should be feasible to change the job setup so that we clamp up three boards on effectively 10.5" wide stock and cut one box all at one go, but that’s a bit more waste stock than I can accept, so we will shorten the box a bit — the top/bottom are fine, we just have to shift the top/bottom a bit.