I managed to get the swimsuit + 1 version in a few hours (seeing as you have to wait 1 in-game day to trade in each doll). It was pretty easy, but maybe that's because I did it with people who knew how to do it.

You just have your partner stay at the moogle to keep telling you directions, trade the doll to your partner - have them trade it into the moogle for the item. Then you stay at the moogle this time and trade the doll to the moogle, etc.

I'm sure there's a different way, but that got it all pretty quickly.

Oh, and to get the +1 version, you just do it all again in a different city.