When they decide to open a moderate, I think CBR is most likely since it's on the skyliner. (Similarly I think AOA and POP would also be next in line.) But that's purely my speculation. And it could be a long way down the road.
Disney was obligated to open the DVC resorts for legal reasons I won't go into. For early July, there are enough vacancies at the DVCs to move all cash reservations there. At this stage, they aren't even opening hotels that are attached to DVCs. That would be the next thing to happen--Poly, Grand Floridian, Contemporary and others will resume using their hotel rooms. It's only logical since those resorts are already partially-staffed to support the DVCs.
Until Disney can justify opening a moderate or value resort, they'll keep relocating people to deluxe. They are upgrading people for free. However, the current policy is that people must keep their original trip dates AND accept whatever upgrade is offered. If you have a reservation for POFQ and they offer a free upgrade to Old Key West, it's take it or leave it. Only other option is to cancel your reservation. It's kind of a harsh policy for Disney, but they're still trying to make the best of a bad situation where they need to restrict park capacity plus there are limits to which hotels they can afford to operate.
And when they remove the freeze on new reservations, expect they won't even offer to book a hotel until they're certain it will reopen. Discounts may also be hard to come by if they're limiting availability and park attendance. Right now, we're in a situation where Disney would much rather fill 3000 deluxe hotels with people paying high rates rather than using discounts to fill 10,000 rooms.