combining OTA and FTA onto one cable

[jorgek]

The misstep in your argument is that you typically cannot use a diplexer pair and a pre-amp in combination as the diplexer pair only passes DC the SAT side so there's no easy way to power the pre-amp.
Amplifying the signal after the loss has taken its toll isn't as effective as boosting before the loss.

What I would do on the OTA side is place the pre-amp at the ant and power it with an inserter then feed the signal into the diplexor and splitters.
Same for the OTA distro amp it goes before the diplexor and splitters and powered via an insertor or into an outlet if near by.
The SAT side in my case does not need any boosting its feeding 1 STB. As I mentioned, the OTA side is feeding 3 TVs and only requires the distro amp.

Hope this clarifies your concerns.