Which tuner is available isn't material unless you configure it to matter. If one tuner is busy recording something, one output can request the free tuner or chase the tuner that's currently recording. Now if one box is recording, and one TV requests a live tuner, the second TV has to wait for either the recording or the live tuner to be freed, but it doesn't matter which happens first.
Yes, that should do it, except that you're missing a splitter at each receiver. It would be between the diplexer and the RF input and output of the receivers. (Three little boxes, a diplexer, a separator, and a splitter behind each receiver.)
Adding OTA would be add another layer of complexity, but it is technically possible. It's also technically possible to use a big splitter to combine the three modulated outputs so that 3, 4, 6 could tune to 1, 2, and 5, but again, that's complexity you don't need right now.