I read this the other day and have been thinking about since then. I'm not familiar with multi part turns, and I didn't get a feel for them after reading the link provide. That said, a couple things come to mind:
First, how many of these ugly intersections do you need to deal with? I have to think (hope) they are the exception and not the rule.
Second, if there are only a few, couldn't you just build a few 'regular' turn features for them and run the impedance up to discourage travel in the particular direction?
I've built turn feature classes, and they are no fun and not easy, but maybe if you just made a single turn feature out of the three you show, it might be the lesser of two evils.
Good luck...
That should just about do it....