Heather, I think your first idea would work very well. I'd braid my round braid around a dowel or something, then pull it out when you get the right length. The moisture content can be the same as when you braid it, but after you pull your core out, don't stretch the braid out, it will colapse without a core until it dries. Before you pull your core, though, take a small board or an equally hard, flat object, and roll your braid out with it. This will set the strings together and give it a really nice smooth look. I'm sure you already do this with your other braiding. It may get upset as you pull out your core, but just lay it down on the bench and roll it out again with a beer bottle or something, being careful not to put too much pressure on it.
Theres my two cents!! Keep us updated, can't wait to see the finished product!