Here in Arizona many of us feed straight alfalfa. I have only come across one horse that gets soft/runny poop from it. And even then, it depends on the batch. The coarser alfalfa keeps her poop firmer than the really rich, fine stemmed alfalfa.
I kind of find it hard to believe a handful would make a horse go psycho. But then again, my yearling is really a handful at times.
I guess what I'm try to say it, don't be afraid of a moderate amount of alfalfa. We (us Arizonians) feed it all the time because it's nearly the only hay we can get. Well, that and bermuda is nearly all I have ever seen. I can count on one had the number of times I have seen any other hays out here.
Alfalfa is generally a high quality, high nutrition hay. It would be an excellent supplement to grass hays.
I've never fed timothy, but I've heard it's good.