Sorry it took me a while to get back to this thread. Obviously, you are looking at feeding for very specific needs so I think a hay analysis might actually be useful. I had one done for less than 100$ (and I'm in Canada where everything costs more). So I know exactly how much protein, sugar, starch, etc. is in my hay, along with things like selenium and other minerals. That's a good starting point.
AS horseluvr2524 points out, alfalfa is a legume so is higher in protein than timothy. Here's an article on timothy: Why Timothy is your horse's friend - Horsetalk.co.nz
It is recommended for horses that may have laminitis. No idea what effect it would have on your horse's hocks.
I feed timothy because my horses don't need additional protein. I feed a hot Arab and a spooky QH mare, neither of which needs extra energy for the light riding we do on them. My Arab also tends to have runny stool, which appeared to be exacerbated by alfalfa.
However, if you google it, you will see that many claim alfalfa has anti-inflammatory properties. So maybe worth a try for you!