Strategies to get good recommendations?

OP, apologies for high jacking. I see you have different questions than I do.

Do you have a GC who will review the teacher recommendations? If yes then they will try to guide the more inexperienced teachers and perhaps get them to clarify something that is unintentionally not great.

There are different styles of recommendation, some teachers will be entirely positive while others will talk about how you did not get X at first but continued to persevere and ended up with a good grade.

It is not that scary. By all means spend time talking to the teachers, let them know your goals and aspirations. You may find them to be helpful in other ways, maybe they can suggest areas you can explore, books you can read. In other words, try to have a genuine conversation with them beyond the college process. Build a real relationship

I’m not sure if my GC will check the recs.

Don’t try to talk to teachers JUST to get recommendations out of them. Chances are, you won’t sound genuine or like yourself. For me, when the time came to ask teachers for recommendation letters, I just reflected back and made a list of about 3-4 teachers whose classes I loved and who I thought liked me enough to give me a good recommendation. You are most likely going to have at least a couple teachers that you just click with, so I think you should be fine.