Meetings are work and are even sometimes productive, no different to banging out code

I agree, and perhaps misspoke there.

However, I find that I have a limit to the number of hours I can program a day, and a number of hours in meetings I can have in a day, but the two don't interfere with each other much so long as I'm taking care of myself.

I think a healthy sustainable mix for maintaining flow over the long haul is probably something like - 4-5 hours coding, 0-2 hours meeting/collaboration, 1-2 hours email, 2 hours reading/writing, 1 hour lunch