HA! . . . We're doing a 4/4 BLT/Kidani in July! We have done split stays before, and as others have said, Bell Services can handle everything. I would suggest that you hang onto your grocery bags and/or boxes, as it will make it easier for them to store and transfer your groceries. We have even considered taking the cloth reusable grocery bags with us this summer to make grocery transfer easier. I would just leave a couple in our OL.
If you have items that you don't want Bell Services to handle (computers, etc), you could try taking them yourself to Kidani and checking those items there. We transferred from Kidani to BLT a couple of trips ago and took a cab with our sensitive items. It was about $20 one way. Luckily, our BLT room was ready when we got there, so we were able to take those things to the room.