I have no idea how that's going to work either, but given Gilliam's awful, awful luck with film productions over the past ten years or so, it's nice to see that he might have a fighting chance of actually finishing this thing and getting it into theaters.
The EntWkly article yesterday explained how it works. It's one of those "through the looking glass" style films. Heath had completed filming the non-imaginary scenes. So now, whenever his character enters the fantasy world, he'll actually appear in a different body (Johnny, Jude, Colin.)