The cot before:
It was a steal... and in the end I bought all three... why?! I don't know.
I decided that I wouldn't waste "good" fabric seeing if this endeavor would work so instead I used an old IKEA beadspread that our dog Scout had nervously chewed holes in when she was a puppy (that's Scouty and the fabric there).
First I ripped the seams of the existing (n-a-s-t-y) fabric and laid it out flat on some butcher paper to trace my template. Then I traced my template onto the new fabric and cut it out and sewed it up.
The hardest part of the whole thing was taking apart the cot to put the new fabric on. The screws were old and tough and it wasn't an easy job to do by myself (there may have been cursing involved. I may have scared Scouty.) but in the end I got it done.