BTW, I noticed that ULINE sells square buckets in black or white. They have a 4 gallon one that is $5.90 if you buy 5 (the minimum purchase). Lids are $1.50. For my address for 5 buckets shipping via UPS ground was $17 something.
The buckets are square in cross section rather than rectangular so about the same width, but shorter front to back as they would be oriented on the bike. The lids are not hinged, but solid one piece.
Not something I am interested in, but I saw it and thought I'd share as another possible option.
https://www.uline.com/Product/Detail/S-13650W/
https://www.uline.com/Product/Detail/S-13650BL/