I would add that indies really are the ideal choice. Prior communication to meeting and advanced scheduling are really key. Also agencies charge a flat hourly rate, so you can easily spend more on the fee than you would with an indy. You need to give the duration some thought as well.
You are right on the mark. To have anything with an agency lady that you can with an Indy you need a record with the agency as a liberally spending client who is willing to invest enough to motivate the owner. There would still be a time constraint unless the owner is motivated to take the escort off the schedule for the night, and still she has to be motivated to go along. Maybe you have met and clicked with her previously. That helps because direct contact with an agency escort without a prior meeting is very difficult, if allowed. Agencies very reasonably want to control the situation to protect their legit interests.
With the Indy direct contact is part of the meeting and setup process, and getting to know each other is desired, not guarded. Her time with you is as flexible and open as she wishes with no oversight. If you are lucky, like I and many others have been, not everything is on the clock ($). Sometimes Indy generosity is amazing. Very good and proven reliable agency clients can negotiate and make some great deals, but everything is accounted for. On the other hand I've never needed to have a record or prove anything to enjoy a great time with a nice deal with any Indy. All it takes is her liking and trusting you during your communications.
Good luck.