buy adjustable boxes...
Say 18x24x3-6-9
The flaps adjust & can be trimmed/folded to make a box of different heights.
Ulne's S-4507 is 26x20 and can be 4"-6"-8"-10" or 12" deep. $1.83 each. pp33 in the catalog
There is space for corner protectors (pp242) too.
pp48 has a cool carton resizer (blade on a stick) to cut boxes down as needed. (not needed with above box)
If Uline is not in your city you may find shipping very expensive... check for a local corrugated box mfger... My local one (Advanced Packaging Specialist) is great. No more Uline for me if these guys can make it. No shipping at all...