UPDATE: Well, it was moot trying to figure out the thing, because when I went back the next day, I saw that the big guy had bit the dust:
BUT.... Charlotte had come along and taken his place, her and her big ol' egg sac!! :-O Caught her feeding on the big guy, and decided, okay, do I love nature more or do I want a big ol' nursery full of little bitty spiders running around my kitchen? Needless to say, they all met the big vacuum cleaner in the sky. I suctioned the whole mess up, tossed the vac bag into a plastic grocery sack, and then threw the whole thing as far as I could into the back yard. If Charlotte was harmless, then she was able to escape. If she wasn't, next time my spider-eating cats go out, she's toast. :-) Thanks to all the respondents! It's been real! ;-)