One of the many things guests can discover if they keep current on the DISboards.
It's a great community of information!
True, but CM's have told me this as well. Most guests trust that information/concierge desk CM's have reliable information about resort packages, and this question is slightly obscure.
OP, we did this on our first split stay too! I asked multiple CM's about getting our tickets early - one the phone before we went and twice at the resort.
Lucky for us, it was before FP+, and our non-ticket stay was just one day.
One potential solution would be getting Annual Passes. I don't know where you go your tickets, but if they are via WDW directly, it may be possible to convert them now to AP's. You would then qualify for the AP discount....which might be better than the free dining discount if your dates match. (You can combine AP discount plus the
DDP, it is just a different discount. You'd get 30% off the room portion of your stay, while adding the cost of the DDP. Plus AP's get a few small bonus discounts on merchandise.
AP's cost more than straight 7day tickets, but- they are good for a full year. If you usually go every year, and can go one week earlier next year, then they may well be a good deal. (Because you'd be able to buy one set of AP's to cover two trips) Often, when we used to go during free dining- ASK!!!- we were offered a 30% off bounceback offer. You have to book it before you leave WDW. (I usually book it while we're waiting in the airport for our flight.

) If you book a great bounceback offer before check out, then you'd really be all set.
But I'm also not sure who told you that you can't book your FP+ until you check-in to the second resort. That doesn't sound correct. You should be able to book dining at the 180 day mark from the day of check-in, and FP at the 60 day mark. Further, for prebooking purposes - your crossover day will be part of the first stay. Guests are allowed- or rather expected - to go to a park on the day they check out. Unused dining credits are good until midnight of the day you check out. So if you check out of BLT on Auguest 10 say- you'd be able to book FP+ on Aug 10 as part of your BLT stay. You'd be able to pre-book dining and FP+ for Aug 11 when the AKV check-in date hits the eligible dates.
I think you'll fully be able to get A&E on your crossover day.