I've got a combination of neck and shoulder injuries on my left side. Neck from being spiked, shoulder from an americana and a west point ride suplex. I've definitely got weakness in my rotator cuff. I intend to get that strengthened before I go back to training tachiwaza, but since once a shoulder is injured, it's always a bit more injury prone, I'm figuring a brace would be a good idea. Does anyone have a recommendation for one that would be good in terms of providing a bit of extra support while still allowing a good range of motion and also not having anything hard or exposed velcro that would make it unsuitable for Judo?
I have a shoulder brace recommendation, but before I give it, I will explain why I don't think it's going to do what you want it to as far as the muscles are concerned.
Your stated injury is in the SITS muscles which are what comprise the rotator cuff. Only one of the muscles actually produces motion of the limb in a plane, the primary function of these muscles is rotation of the arm. The brace is going to do nothing to help that, and may actually make the muscles work harder as they have to rotate the limb against a resistance.
Where the brace helps, is preventing over stretching and extreme motion, which will protect the ligaments in the shoulder, and to some extent the muscles from tears.
The shoulder is barely even a joint, and is the most vulnerable joint in the body simply because the structure has to allow such a wide variation of movements. This means any injury is going to really make the structure vulnerable to more injury.
I will second @trevoke on the don't work it until healed, and I know you said you will rehab it first, which is good. Once it's fully rehabbed, I would recommend the SB04 shoulder brace by EVS sports : http://evs-sports.com/store/product.php?productid=17697
It bases the support going across the body as well as directly down to a strap that goes around the entire chest. It includes an impact protection plate over the shoulder, and is very adjustable. While nothing will fully protect (Especially in an arm intensive art such as judo), this is one of the best I've seen in use. I would get a lightweight close fitting tech tee to wear under it to prevent chafing, though.
I have no shoulder brace recommendation.
My recommendation is to stop all the practice that requires the use of that part of your body and go to rehab instead. I'd recommend soft movements like taichi or chi kung because of their particular health-building properties, if you want to heal faster (though it requires finding a skilled teacher).
Again - stop practicing entirely. Would you rather be out for a few weeks to a few months while this heals, or potentially be out for years or a lifetime if an accident happens? An accident, by the way, could be you lifting your arm the wrong way, or it could be you taking a bad fall for whatever reason.. Too many ways to damage yourself.
Take care of your body. You only have the one.
I'm with Trevoke on this one. Take it form a judoka who is a mess of never properly healed injuries, strains, and arthritis . FIX IT FIRST! Don't train until you get the all clear from a GOOD physio therapist and it's 100%. I might not personally recommend tai chi because i've never done it. But some yoga and perhaps running or something like that to keep your cardio up in the mean time.
IF you insist on training anyway: Put your arm inside your gi. and tie it to your body. Do judo one armed then you can't make a bigger mess of it. You can't do everything this way, but it'll help keep you active, and you can work foot work drills, and some uchi komis and the like.