You CAN do what you describe, with a few caveats:
1) Each member is only permitted two active waitlist requests at a time. Each night you waitlist--or string of consecutive nights--will be a separate request.
2) There's always a chance that your missing nights will not be filled. Are you willing to take the chance that you'll have to switch resorts multiple times during the stay?
Disney hotels average about 80% occupancy so cash guests rarely find that they cannot get what they want. Even when booking on short notice, their property-of-choice often has many different categories / views available.
By comparison, DVC properties operate near 100% occupancy. The more popular (and smaller) destinations will consistently approach that 100% occupancy level more than 6 months out. BLT definitely falls into that category.
There's no harm in booking what you can now and waitlisting other dates. However, every waitlist success requires a cancellation. If nobody cancels the dates you're seeing, you simply won't get it.
If you're booking at least 7 months out, it's typically worth a shot. Book what you can and set-up the waitlist. But if 2-3 months pass with no movement on the waitlist, you may have to seriously consider alternatives. Resorts like Saratoga Springs and Old Key West are typically among the last to fill. As your trip dates draw closer, you may have to decide between the split-stay with multiple resort switches or just moving your entire reservation to a resort which has availability for the full time.