Can I have the best of both worlds, F-Type connection and wireless?

[old_tv_nut]

OK, I didn't realize your full set up.

I think I would recommend trying the following:

Modulators --> combiner --> distribution amp --> two way splitter -->one output to transmit antenna, the other to passive multi-output splitter for wired connections

or:

Modulators --> combiner --> two way splitter, one to amplified or passive multi-splitter for wired connections, the other to distribution amp and then to transmitting antenna

Also, I would get some in-line attenuators in case the path feeding the wired connections overloads. Do not attenuate the path to the distribution amp and antenna, where your goal is to get the largest possible signal.