Although members can transfer points to each other you can only do one transfer either in or out per year, so you couldn't both swap points in the same year. It could be possible that you both booked a reservation for each other and swapped reservations, but this would involve a lot of trust so would probably only work with someone you know personally.
The best way would be to do what you suggested and to rent your own points out then rent the week at BCV, although I'm assuming you don't mean for September this year given how close that is?