I know the payphone is an outmoded (and rapidly disappearing) piece of technology; but I was wondering if any hobbyists out there use it to fulfill two-call. Or is a burner phone the more feasible (if less cost-effective) option?

likely there will not be a pay phone there.  Secondly, a cell phone comes in handy when the provider wants to guide you, turn by turn, to her location.  It isn't always just a room number that you are given on the first call.  Lastly, I carry the cell phone with me while going to her room.  On several occasions (in over 13 years), I have had to retreat and call again because the booker gave the wrong room number.  In both cases, luckily there was no body in the room when I knocked on the wrong door.

...the one payphone I've seen in the last 6 years is no longer there. If you were to depend on that you would be SOL nearly all the time.

So I would definitely not Use a pay phone there's really no way to call back and I would just feel uncomfortable about that kind of situation to be honest...

They often times show up as restricted or # unavailable. Many ladies won't even answer the phone under those circumstances.

I decided to buy a burner.

I have used Google Voice with my regular phone, but I deleted it recently b/c they are collecting too much info (hobby and otherwise) from me. Since I am not a tech expert nor the most careful person, it makes me uncomfortable. They are just too good at what they do. Another thing is their sound quality and their ability to stay connected are not very good.