We love to "counter program" the crowds as much as possible.
So we eat a big (and late) breakfast, so that when we get on board we know we won't be eating lunch until 1:30. At 1:30, Cabanas is EMPTY. So is the sit down. Meanwhile the rooms and hallways are swamped at that time so we avoid the rooms then. Once we finish lunch, then the hallways to the rooms have emptied out.
As for the luggage, it is a pain. Putting them under the lunch table is no fun, but doable. Depending on your situation, you might be able to do what we do. One person finds a nice comfy lounge chair somewhere in the shade, we PILE all of the carry-on luggage with them, and then they just sit there and relax and "watch" the luggage while the rest of us go off unfettered. We often bring food to that person, or we can come get them and lug the luggage to dining room. Whichever they prefer. It really is a nice win-win.