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You understand that for Low Dollars as in 3 , 4 , $500.00 or so , no perfect solution will be found , compromises are the way it is.
With channel filters and channel modulators changing a channel to another channel and then inserting the channel/s in to distribution system and equalizer s and more and dollars that are thousands , you will get closer to getting all that you want but not all.
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Here are some more alternatives.
www.slingbox.com , a slingbox a tuner a antenna at the location that you want to receive channel/s , and stream the channel/s over the Internet to your , computer / Tv.
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www.aereo.com
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Some Tv stations are , streaming over the Internet.