If you want to buy and visit both AKV and BCV, I would buy at BCV. Reason being, for your spring trip it's probably 95% likely that you can find what you want at AKV with BCV points. AKV is very large, and often one of the 3 most available (along with SSR and OKW). I booked a stay at AKV last year on a months notice, and got a Grand Villa at AKV last november at 6 months.
Conversely, AKV points will yield only moderate success at BCV at anytime throughout the year as BCV is really the hardest resort to get a reservation at. I would not say it's impossible that you could get something during F&W at BCV with AKV points, but it's certainly going to take some work and require you booking at 8 a.m. online at the 7 month window. Even then, you are looking at maybe a 30% chance?
Just as an example, I am a BCV member and looked at 7.5 months (2 weeks before the 7 month window) for a weekend at the end of October at BCV, and it was not available. Some people buy at BCV exclusively for F&W. So if I as a member couldn't get a room over an October weekend outside of 7 months, then that should give you an indication of what might happen as a non-member. Of course things change, there are always waitlists and some people do have success.
All things being equal, I would think just buying at BCV would virtually guarantee that you'd be able to get both your spring AKV room and October BCV rooms with little problem so I'd consider going that route.