Having moved 8-10 ton of records from WV to VA, I speak with some experience.
I agree; the 10x10x10 (or slightly larger) are fine for loose 10" 78s. The 12x12x12 are good for loose 12" singles, and , of course, LPs. I used 10" and 12" LPs as filler on the sides of all boxed singles.
As for albums (folders of 10 or 12 discs, filled) I too wanted them saved. I used the 12x12x12 bowes into which the 10" albums fitted nicely. To adjust for the height, I cut the boxes down from the top, so as to form a tight fit.
Strapping tape is a must. Note: on ALL boxes, I opened the bottoms and RE-SEALED them with carpenter's glue, weighted for a time with a concrete block. Then used tape to ensure the bottom.
I may have broken one or two discs during the transfer. Otherwise, everything held up OK.