is there a family member who would loan you the money just for a month?
approx $10k to cover the new car plus the loan difference on the Pilot
to be paid off, in full, when the Pilot sells.
that way you don't need to finance the new car, and you solve the puzzle of how to pay the extra $k or whatever the Pilot loan requires.
the hypothetical family member would be quickly and fully paid back, and you'd have the cheaper vehicle, no car payment, and the $6k or whatever the difference is in vehicle value.
If not hypothetical family member, you might just be stuck with this until you sell off some asset to raise the $3400 yourself, and that's OK too, it won't be much longer and at least the car payments go vastly more to principal than interest, so you're making some progress every month you make them.