I would leave it in the holder and send it to PSA. You can designate the lowest acceptable grade say a 6. They will evaluate the card in the holder and if they feel like they cannot bump your card, they will send it back in the holder with a voucher for your next grading.
If SGC made a mistake I'd imagine that PSA would enjoy correcting it for a possible new customer
The idea for resubmitting to SGC is also a good one. For some reason PSA graded cards sell higher than SGC. I assume it is because more people collect PSA registry sets than SGC. It may be worth it to them to pay more for the PSA card than buy the SGC card and possibly downgrade during crossover.