I figured out a solution that worked well for me. I created a text file that contains every room layout, back to back. It is referenced using AJAX. Each room layout consists of 120 characters, so I'm using "mid" to reference a random level layout like so:
mid ( ajax.LastData, ( whichLevel*120 ), 120 ), where "whichLevel" is a random number from 0 to [total number of layouts I make minus one.]
I am using a spreadsheet to make sure I don't lose levels in the giant text file.