I don't know of any of the modulators that have a 300 ohm output. They all have coax 75 ohm. You could add another adapter to convert to 300 ohm, then you have to have 300 ohm flat wire. For what you are doing, zip cord would probably work in place of 300 ohm flat wire.
If you have to buy an RF converter, why is an extra couple $$$ such a big deal for the F-fitting to 3.5mm adapter such a big deal?