[kremdela]

I mostly solved this problem by taking 2 minutes and writing a thoughtful response to remind them that I am an actual human.

"Thanks, COMPANY_NAME sounds interesting, but I'm not looking to make a move. I really enjoy working with my fantastic team solving challenging problems in my current position. It would take an unbelievable improvement in [salary, schedule, problem space] to make me consider a move. Let's stay in touch on LinkedIn and feel free to reach out in N months or if any amazing opportunities that meet those criteria come across your desk. Thanks!"

Personally, I have found that not all, but many recruiters will reply with a LinkedIn request and an "I'd love to get to know more about what you are looking for, or will follow up in N months."