As I said, you can ask a Cast Member to take the picture or even a passing guest.
My story - many years ago, my mother-in-law and father-in-law took my husband and me to Disney World and we stayed in a great suite at the Boardwalk because my mother-in-law wanted to see "the ball" every night. It was the one time we were spoiled at Disney World. My father and stepmother lived just two hours from Disney World so I arraigned for them to surprise my in-laws by just showing up (my in-laws and my parents have always been close, so much that they did things together without us even knowing!). Anyway, the arraignment was that the in-laws and my husband and I would go to breakfast at, I think, Spoodles. It was a late breakfast and we were seated at a nice table for six. Because my dad and stepmother were already there waiting for us! My in-laws were shocked! After the breakfast, I wanted a photo of all six of us together on the Boardwalk. My father-in-law said it couldn't be done and we were not going to pay for it. I said, "trust me". I just walked up to the DVC guy at his little booth and asked him if he would mind taking a photo. He did without hesitation and even posed us. It's one of my favorite photos of all time as two of the people are no longer with us.
) I'd absolutely bring some fast (read: heavy) lenses and a flash into the park one day and take a few pictures in exchange for a Mickey ice cream bar. Assuming you just want a few shots for cards or some such, it shouldn't take horribly long - and besides photopass or the expensive $1700/hr options, that may be your best choice is to find an amateur who's willing to do it. I couldn't do it for everybody (besides, Disney would get suspicious and I can't eat that much ice cream!) but one couple isn't outside of the realm of possibility for somebody just taking a minute of their own time to be nice. 
