Ok, I know it's not the preferred route, but I went ahead and bought a strop off of ebay thinking that I would probably cut it all up and ruin it anyway so I didn't want to spend much.

This is the one I got except I got it from a different seller for only $12:

NEW PROFESSIONAL 21 IN LEATHER BARBER RAZOR Strop Strap | eBay

First off let me say, this thing is junk. But that's what I expected. The leather is some sort of pressed leather with a faux leather strip on top of it. The draw was nonexistent and it had no feedback at all. It was like dragging the blade across plastic.

So here's what I did: I flipped the strop over (the hardware is removeable) to reveal the underside of pressed leather. It was quite fuzzy so I rubbed it down with a pumice stone until it was relatively smooth. Then I rubbed it down with a dry puck of col cronk's soap to give it a nice smooth feel. While doing this I intermittently gave it some vigorous rubs with my palm to melt the soap into the leather. What i ended up with was a smooth but somewhat sticky strop. The draw was a bit too much now so I put some water on it and rubbed out the soap some more and now I have what I consider to be a fairly ok strop to start out with. It gives me a nice smooth resistance with a good smooth scraping sound (when I use a proper stroke) and a distinct ringing sound when I use too much pressure on the edge.

With this strop I've been able to keep the razor feeling pretty much like it felt when I got it in terms of how it shaves. Now I'm only 2 weeks in right now but I'm still not cutting myself and I'm getting closer and closer shaves out of it so I believe the strop is working just fine. It's certainly not ruining the edge.

I just wanted to post this as a tip for anyone else out there who went cheap on their strop or bought one before they found this site (like me). If you've got a cheap strop that doesn't seem to work very well, don't give up on it. See if you can make it better. The worst that can happen is you ruin a nearly worthless strop and have to buy a better one anyway.