Two thoughts:
1) If it were me, no question about it, I'd stay at a Disney Value resort that night and barely unpack. In the morning, I would have the resort transfer my luggage to POFQ while I hop on a bus to whatever park we want to start with. Waking up in the magic and getting right down to serious fun would be my best option. I want to avoid the delay and the bother of getting transportation to either the airport or to POFQ directly. Using the plan I described above, when we were done in whatever theme park we would simply take a bus "back" to POFQ and check-in at that time.
2) $300 additional for one night at POFQ? Are you sure? By any chance, do you have the dining plan booked? Because that might explain why the room seems so expensive for one night. If that's the case, then I suggest you try to book a separate, one-night room-only reservation at POFQ for that Saturday night. That way, you won't have to pay for the extra day's worth of dining plan entitlements. On Sunday morning, you would have to check out and then check in again at POFQ's Front desk, but even the farthest room in the resort is only about a 3-minute walk from the lobby ... a lot less bother than switching from an off-site hotel. Chances are you would not need to change rooms in this process, but it is possible.