Personal project for my backyard... which way to choose?

I would either do option 1 or 3. With option 1 the signal is boosted between each post. With option 2, you will have really long runs and may have issues with data loss.

If you have good line of sight between the posts, option 3 should work. If your house is blocking some, UDP may have issues keeping them in sync. But you could set something up on your computer that sends an API request to each node to change settings.