Lady B -
Just some thoughts...
Check curbsides the night before bulk pickup day, check upscale neighborhoods first.
Chat with the collection driver/helper that services your area. A six-pack might get you a 10'x12'.
Post a (shudder) wanted poster in local supermarket or launderomat.
Check with a local rug merchant for remnants.
There is much written in novels regarding captain's quarters floor being decorated with painted canvas, checks mostly but a compass rose might do very nicely.
Jas. Hook