I agree that a spectrum analyzer is the ideal tool, and when it comes to narrow signals like beacons, that can even be done with a cheap SDR and a laptop. There is however one very common problem with using the beacons: very often they are using the "other" polarization type. For example, on 22W, according to what's published, the C-Band transponders are circular, but the beacon is linear. And on Ku, the TPs are linear but the beacons/telemetry are circular. There does not seem to be any hard rule about it, some satellite use the same type and other use the opposite type and some use a mix of both. They can still be used to peak the dish, but might not always be useful for peaking the dielectric,
It might be better to look for a transponder that the spectrum analyzer can display together with the surrounding noise floor (so if using a cheap SDR, a very narrow TP that would be at most 1 MHz wide. Not every satellite has that though)
where do you find such Teflon sheet?