how can skill sessions (i.e., bullpens, control drills, new pitch practice, etc.) be integrated into this time period?
With great care! One key to all of this is how your son’s arm/body feels. When tired/excessively sore, more rest is indicated. If the arm/body feels good, keep going. Any of the above skill work you want to do can be done on weighted ball throwing days, prior to the weighted ball throwing. Do the least amount of skill work throwing as possible while doing the TV training. You will have to prioritize the goals you want to accomplish, i.e., improving mechanics, learning a new pitch, increasing throwing velocity, etc., and train accordingly.