BF's parents said yes! They said they did not have a problem with the dogs staying the weekend! I was completely upfront with them, discussed their anxiety issues and behavior patterns, and reminded them that it was totally okay for them to say no, that we would find another option. I even offered to get baby gates and gate off certain rooms of the house, but they said it was not neccesary.
They agreed to it because, coincidentally, they were going to be away that weekend anyway. Their only stipulations were that BF and I would be responsible if the dogs accidentally break something, and they requested that we vaccuum the downstairs area after the dogs leave because BF's dad is slightly allergic to animal dander (something I did not know until BF's dad told me. All I knew was that he was allergic to cats). Both my dogs have hair, not fur, but one of them sheds minimally, so of course we agreed.
My mom disagreed that it was neccesary to bring the dogs over ahead of time so they can adjust. She said that they already know and love BF, and the fact that either he or I will be with them the whole time, they'll adjust quickly.
Also, it turns out that the Friday work issue will not even really be an issue after all. I go to work from 8 to 5, and BF's schedule ended up being 5 to 10. So I am going to arrange to leave from work an hour early, which will give me ample time to get to BF's house so that he can leave on time. We've already planned the day on Saturday, and it revolves around the dogs. There is a dog-friendly park about 10 mins from BF's house that we plan on taking them to - unless, of course, it rains.
Anyway...this turned out to be a lot less stressful than I thought it was going to be! Thanks for your advice/support/encouragement!

170 Invited (holy crap!)
98 are coming to party!
29 have other plans
43 need to respond!
"Bside - You're just too sexy for your own good" ~ leia1979
"True love = I still love you even though we hang out all the time and most other people would be tired of each other already" ~ flygirlmeg