My son also has a similar situation. He has 3 D1's interested in him, and they are all saying that the #1 thing he needs to do is get faster, so that it is his priority this offseason. He is working on getting stronger, too, but these teams have watched him enough to know that he is not a power hitter, and he's only a part-time pitcher. They have been very clear that what they want to see is more speed.
He is a 3-year starter on the HS team, but there is a new head coach. He did not play on the HS summer or fall teams because he played on his travel team and we learned from years past that it's not productive for him to do both.
He is doing 3-day a week baseball-specific speed and agility workouts with his travel team, and baseball-specific lifting on other days (he has the Angels off-season workout book). There is already a huge difference in his speed and agility after just a few weeks. But has been getting pressure to work out with the HS team. Like dad43's son, he is a junior and will be counted on as a team leader. So he went to the last two workouts. They consisted essentially of calisthenics and long-distance running. This is not going to help 2B get where he wants to go. But he feels the pressure from the HS team and wants to do the right thing, so he is doing both. I told him it is up to him. What will suffer is his lifting program.
I agree with everyone here who says to communicate with the coach. I disagree that the HS coach is the boss, but then I am a little jaded because we've had 3 coaches in 4 years. In my mind, the HS coach is the boss during the HS spring season, but in the offseason, you should do what is best for you.
swva - the tough choice, as you already know, is deciding what is best for you - be with the team, or do the workout that will better help you develop for the future. Or try to do both.