It would be a lot of work making it fit. There is the cord at the top to hold it to the trailer that would have to be sewn in, and another one on the bottom to hold it to the roller. Also, most tarps are thicker than awning fabric, so it may not fit in the slots you have, plus it would roll up thicker on the roller.
The good news is the Carefree awning fabric is a lot cheaper than the fabric for Zip Dee.
Meddle not in the affairs of dragons, for you are crunchy, and taste good with ketchup.