Tbh paying to see them more is about as far as you'll get here. You're paying for a service. Sex workers typically have multiple bookings a day, and already have regulars who pay for over an hour a week. Outside of that, they have their own social lives that they have absolutely no interest in mixing in with their work for obvious reasons. Many also have boyfriends who either don't know or do and watch out for their wellbeing.

You can find someone who's pleasant, but fundamentally it's transactional - you're paying for a service for a given period of time and nothing beyond that. There are plenty of books on this if you wanted to know more, Louis Theroux just did a doc about it too, but that's pretty much what you'll find out all round

Even if you did manage to game some escort into fucking you for free, what then exactly?

It's odd to me that you were so resistant to the idea of creating a social circle, which would make things easier for you both inside and outside that circle, but you float this as if it's a plausible idea. Trying to game an escort from cold into seeing you on a personal/romantic capacity is one of the most stacked against your favour game scenarios I could think of.