I would like to complete an artwork sized 22.5 feet x 15 feet in Illustrator but can't because Illustrator has limitations on artboard size. How can I circumvent these limitations?
You should ask your print house, but it's probably fine to deliver artwork at 1:10 scale.
So I would simply set up my document to 2.25 feet x 1.5 feet and tell the print house to print it ten times larger.
Beware that any images of course will be printed at 1/10 of the effective resolution you deliver them in.