So here's a question then, can you split your stay?
Yes anyway you want at as many resorts as you want as long as you have the points to cover it.
By that I mean book part of your trip at the one resort and then move to the other?
Each Home Resort you own at allows you to book at that particular resort during owner's priority booking window ( 11 mos thru 7mos+1day before checkin you want)
Can only 1 of them be booked at the 11 month window being designated as your home resort and then the other at the 7 month window if you're luck to have availability? I'm assuming that even if you own equal points at each, one has to still be designated the home right?

Each and every DVC resort you own at is a "Home Resort" - - if you own 100 points at BLT that give you Home Resort priority booking there for up to 100 pts 11 mos-7mos+1 day before checkin date you'd want at BLT; if you own 100 pts at AKV same thing applies there - you can still book there at owner's priority booking window but only using your AKV points. You cannot use BLT points to book at AKV until 7 mos or less before checkin date, etc. You can't use BLT or AKV points to book at any of the other DVC resorts until 7 mos or less. And you would not be able to use BLT points combined with your AKV points to cover a night of your reservation at either BLT or AKV until 7 mos or less.
At 7 months or less all points regardless of what Home Resort they are tied to become "equal" so to speak and may then be used to book at any DVC resort.
Members who own points at more than one resort often alternate stay EOY or ETY at their resorts by using banking &/or borrowing - - if you banked 2009 UY points from BLT into 2010 UY you would have double UY allotment of BLT points to book BLT with for a trip during your 2010 Use Year at 11 month owner's priority booking window ( triple UY allotment to book with at 11 mos owner's priority booking window if you both banked 2009 & borrowed 2011 UY points )