So here’s my experience so far.
I saw the HD has Heavy Duty Small shipping boxes. Higher ECT than some of the others, and 12x12x12 - seemingly perfect. I went and bought one to try out. The inside is just a touch too small. The records won’t slide in edge to edge. So that’s out. I stopped at U-Haul and got one of their Small Shipping Boxes. Regular jacketed records fit perfectly, but anything in a box set case will not. No matter - as @mijostyn suggested I can just get the few slightly larger boxes I’d need for those.
The problem is that if the U-Haul box is completely filled from one side to the other with records, the fold-in handles will rip away from the weight of the box. It turns out that the handles are just good enough (to account for any chance of rough handling) holding a stack of records about 12x12x12. So I think that’s what I’m going to do moving forward, putting the records in the center and using peanuts or small soft items to stuff on either side.
The U-line 13x13x13 boxes would seem to be perfect, but the shipping is cost prohibitive. If I had a 10,000 record collection that might be one thing, but for the 20 or so boxes I’d need I’d pay close to same amount in shipping as the price for the boxes. This may or may not be useful to anyone else.