I really goofed up.
Here I was, with a bunch of hatched silk cocoons. I'd found good instructions for cleaning and de-gumming the cocoons, and was excited to try spinning the silk. I treated the silk like wool, and carded it in preparation for spinning.
Don't do that.
It was clear to me right away as I was carding the silk that something wasn't right. When I spun, the results were lumpy, irregular and just not pretty. So I consulted my good friend Google (as I probably should have done in the first place.)
Wormspit.com came to my rescue again, with the best instructions I've found for preparing hatched silk moth cocoons for hand-spinning. Another nice resource when it comes to actually spinning the silk is this article on Knitty.
You can see in my photo, the yarn on the right was my first attempt to spin the silk, and to the left was my second try, after my research. Probably still not the best silk spinning ever, but a huge improvement, if I do say so myself!