Actually, I did find a way to do it that was fairly simple, it just involved being a bit more careful. I used a bowl and pressed the water out with my hands so that the fiber didn't get disheveled, and then coiled it in such a way that removing it wouldn't cause a tangle. I tried the strainer with larger roving and it didn't help, because the fiber floated around in the sink and that is where it became too loose, but this seems to have worked well.

We had a power outage all last night thanks to some bad windstorms (more windstorms tonight, actually, I am surprised the lights are still on) so I wasn't able to post, but I have a great pictorial on the successful process to post.

I haven't seen one like it online, so I feel like a bit of a pioneer ;)