Hello! Welcome...
Well, don't take this wrong but I'd like to make some comments to your post.
TV preamps are 75ohm versus the 50ohm impedance your repeater is more comfortable with. What does that really mean? An impedance mismatch means less than desirable performance.
The fact is, preamps and receiver front ends rarely actually meet whatever their specified input and output impedance is supposed to be. You might be able to measure differences in otherwise identical preamps, but in practice, it's not likely to be noticed. If you look at the input and output return loss specifications on even high end preamps, you'll see that it can be pretty dismal. Preamps are usually matched for minimum noise figure, and that can be mutually exclusive of best match at 50 or 75 ohms.
That being said, give it a try. Although, before you do, I recommend doing a little math first... A good rule of thumb is to assume there will be a .5db of loss per connector (approx), PLUS whatever loss is incurred through the filtering circuit (pre-selector/receiver multi-coupler/duplexer) PLUS whatever loss occurs through the interconnecting cables. Add it all up and you have a rough idea of how much loss you need to recover to get back to where you started.
0.5 db loss per connector is actually way high for properly installed connectors. It's more like 0.1 db per, or less.
For example, start with a -100db signal (distant station) and ADD -5db of loss for 4 RF connectors (-5db x 4 RF commectors- feed line to polyphaser to multi-coupler to receiver) and we get -120dbm (not good).
Your math is WAY off... 4 connectors at 0.5 db would be 2 db. You just did 4 connectors at 5 db for 20 db loss.
-120dbm is well into the noise floor and past the signal/noise threshold. But don't fret... we can remedy this by throwing in a handy dandy 16db preamp and bump our loss back up to -106dbm (not bad).
That would bring you to -104 dbm, but that's actually not really significant. In the case of a preamp, it's really all about the noise figure, and not so much about the gain. The preamp noise figure MUST be lower than the receiver noise figure, or there will be no weak signal improvement. The gain needs to be just enough to overcome the receiver noise figure, and whatever losses there may be between the preamp and the receiver. Too much gain can put the next stage into compression, and that will destroy the total receiver noise figure.
Sounds good huh? Well, not always. Pre-amps don't just amplify weak signals, they amplify the garbage too. In my experience pre-amps can be a real pain in the back side. I only use them to recover the loss I incurred from the coupling. Bottom line- match your loss.
Long story short, give it a try. BTW, be sure and change the connectors out on the preamp to something a little more 50ohm friendly (so239/bnc/-n-/etc.).
Well, this is true. Preamps CAN be a pain in the ***, but that's usually because they are seriously misunderstood.
One last comment about the adapters... again, the loss is about 0.1 db per adapter, so as long as you don't over do it, below 1000 MHz, adding an adapter to a cable is insignificant. How do I know? I measured a TON of adapters and connectors.