First baseballinstruct I think it is a great thread you started and it is good to have a place where questions can be asked and answered. You certainly have the resume and it is great you are here.
I thought the same thing as JH when I saw your post regarding post recovery. 4-5 years ago it was considered appropriate to run 2-3 miles after pitching "to get the blood flowing for recovery and removing the lactic acid" and it was standard practice and it made sense at the time. Well now 5 years later and with more studies done on the subject distance running for baseball players is not considered the optimum, there is no such thing as lactic acid caused soreness in pitching. Same thing with weighted balls, lifting for pitchers, icing, 120 ft throwing limit, etc.
My point is that I think it is important for you, if plan to do this as a profession to read up and discuss with the real leaders in the field. Ron Wolforth, Kyle Body (driveline baseball) Eric Cressey, Bret Strom, are just a few that are taking a hard look at what has been done in the past and questioning and challenging what athletes are told to do, "just because that is the way it is done"
From my reading on the subject (and I am not an expert by any means) the modern thinking is that:
1. Distance running has limited benefits for baseball players, and in fact makes them slower.
2. Weight lifting for pitchers can make a huge difference in velocity and longevity.Quick question, What is the single best lift a pitcher can do? Who would have thought it was a "deadlift". (at least not me anyways)
3. Yoga is great for the general population for health and flexibility, but baseball players are better off doing specific stretching and using micro rolling to improve flexibility where it is required.
4. Weighted baseball programs are not only beneficial in velocity development but recovery.
JH provided some links but I would encourage you to read and be in touch with your peers particularly the ones that are really questioning historical practices and are trying to understand what is optimal. These include P3 sports in Santa Barbara, Eric Cressey, Drivelinebaseball, Wolforth, and others.