It's tedious, but you have to select each connector one at a time (note: not each shape), in the order you want and "bring it to front." My drawing is a top-down tree, and I started from the (what I wanted to be) the leftmost leaf, worked up to the root (top) and then down the other side, staying connected the whole way. After setting the order this way, deselct everything and do the re-layout.
In general, any shape you want to move to the right, select its connector and "bring to front." But unless you do them all systematically, it will be hard to set an overall order this way.
I also tried to speed up the process by multi-selecting the connectors in the desired order, and then doing just a single "bring to front." However, I couldn't figure out what orderings this was producing. And there's the danger that you miss when control-clicking on a connector and you figure you should start over because the "order" isn't being set any more.
Hope it helps.