Don't do the Bjorns, they aren't very good for hips or spines and you're likely to get very tired and both of you will probably get uncomfortable quickly. Your littles have got to be getting to the Moby's "limit" (in quotes because Moby's official weight limit is higher than when they tend to start sagging) and could be way too hot depending on when you are going.
Better options for full buckle carriers are Ergo, Boba, Beco, Kinderpack, Catbird Baby, Action Baby Carrier, Lillebaby, Onya, and Tula. My preference is the Boba (I have the 3G and the Air). It is super comfortable and easy to use. It's also got a tall back and foot rests so older toddlers can ride more comfortably (this is a downfall of the Ergo, the body is short so many toddlers outgrow it by height way before weight). My only complaint is that it doesn't do a front facing out position. While I wouldn't use it very often (not very comfortable), it would be nice to have if I *did* want to use it. I intend on bringing the Air for quick trips in and out of places.
Woven wraps are super comfortable, but kind of complicated and take more time to get situated. That said, I plan on bringing my Girasol Snow Diamonds with us in September and am considering making it my primary carrier while we are there (back carry to get to the park, hip carries between rides, front carries on rides (facing in or out, depending on the ride), and front carry facing in on the way back to the resort since I'm sure DD will have crashed completely by that point. I may also bring a couple of DIY gauze wraps, which tend to be cooler and might use those more during the day. Besides Girasol, other good brands are Wrapsody, Didymos, Natibaby, Vatanai, Oscha, Hoppediz, and Elleville.
Then there's the mei tai, which is kind of a cross between the full buckle and a wrap (and there are even mei tais that have buckles!). It's got the body of the buckle, but the straps of a wrap. It'll also be cooler than both because it uses less fabric overall. I am considering going this route as well, but I would be making my own. Brands are too numerous to name. Some popular ones are Kozy, Catbird Baby, Mei Tai Baby, plus wrap conversion mei tais like the Didytai and Hoppediz Hop Tie.
Then there are ring slings, but I can't offer advice there because DD would always become hysterical when I tried to use them and I never got into them after that. I wish we could though because I have a feeling those would be fantastic for inside the parks. Easy in and out, not much material, folds up nice and small. Who knows, maybe I'll give our Maya Wrap another shot.
If you made it this far, hooray!

Clearly I am still on the fence about what I'm going to bring. I wouldn't be shocked if I bring them all and figure it out as I go along.
