Let me preface this by saying that my grand total of coaching experience amounts to 2 practices this year before everything got shut down (long story as to why and when combined with a school district that is painfully slow with hiring made for a really short season), so a lot of my thoughts are theoretical rather than anything I can say actually worked).
I was supposed to spend this spring working at a small rural Title 1 school here in SC. The school typically has some decent talent but has lacked depth and in my opinion quality coaching at all levels going down to youth ball. The biggest things I noticed that we lacked were physical strength and fundamentals. We don't really have much of an opportunity to work with kids in the off season here thanks to state rules that basically limit work to the summer and 20 practices between December and January (that I'm not even sure if our program uses).
Given all of the extra time I have had on my hands the past few months I have been thinking a lot about how we could improve our program so I will share my thoughts since it seems like we are in sort of similar situations.
1. Emphasis the weight room, while inspired by my program's particular lack of strength I think a good strength program plays a big role in any high school athletic program .
2. Pre-planned practices. I would have practices and workouts planned out as close to down to the minute as possible and have the practice plan posted in the locker room or dugout for players to see before going onto the field. I think it would help keep kids focused on the current task and in general will give the kids a sense of organization (in my experience it is really hard to excel when it seems like everything around you is being done on the fly).
3. Emphasis efficiency. I think one of the bigger issues facing baseball is that kids tend to get bored because the game itself and a lot of practices involve a lot of standing around. Limiting idle time could be huge in getting buy in from the kids. I would try and focus on drills that could be "player led," to free up the coach(es) to actually coach as opposed to running the drills. I would also try and focus on working isolating parts of a play as opposed to the whole play at times. What I mean is instead of the coach standing at home plate hitting grounders to the infielders who then throw it to first and then having the first basemen throwing it to the catcher who then gives it back to the coach to start the whole process over again, maybe just have the coach hit grounders and have the infielder field it and only go through the foot work of the throw but then toss the ball in a bucket. This would allow the coach to go faster allowing more reps and lessen the chance of an errant throw or hit taking out a kid that wasn't paying attention. If you have multiple coaches that can hit fungos doing some split field work should also help improve practice efficiency and help problems caused by lack of space or facilities.
4. Measure and track whatever you can. You specifically mention kids not thinking that off season work is worth it if you can find a way to measure something (anything) then you will be able to specifically show them improvement which could lead to better buy in. If you could find a way to fund raise enough money to buy some kind of technology that can give you some insight into what is actually going on with the ball it may lead to the kids having a better understanding of what is going on when they do certain things on the field. This goes for the weight room too, assuming your kids are actually gaining strength it is really easy to keep track of growth and show kids their improvement.
5. Try to create competitions and competitive environments. Competitions within practices and workouts can also give kids a benchmark that they can measure their improvement and can give some kids the motivation to actually put in work as opposed to just going through the motions. If possible think outside of the box and try and do some things that may not necessarily relate directly to baseball and possibly allow some of your "lesser" baseball players to have some success.
Sorry I don't have any specific drills or anything for you but ways to improve a program have been on my mind a lot recently (I blame it on my virtual baseball clinic overdose during the shutdown).