I know what you're talking about, I just haven't done it so here are my thoughts, whether you want them or not.
With Thangles, the sewn line goes to the corner on one side and ½" short of the corner on the other (not the cutting line as you have it drawn). The lines are not sewn zig-zag with Thangles, but it might work your way. The measurements they use are to add a ½" to the finished measurement you want. IOW, a 2½" strip will give you 2" HSTs. It might be worth a try...
This may help you see it more clearly than I described...
http://www.sews.com/quilting/thangles/thangles.html
My personal guess would be that it would not save any time because you will lose both time and accuracy on the pivot points, but that's just my personal guess. I do know people say Thangles don't really save any time.