It doesn't seem possible anymore to book a room at an upscale hotel with privacy.
The steps that need to be taken seem to be to much.
Even if you use a green dot card didn't you have to have the green dot card mailed to you. If you set up a mailbox don't you have to pay for that as well?

How is anonymity achieved anymore?

You will still have to put a credit card down at check-in but nothing will be charged to the card if there are no additional room charges during your stay.

Total privacy is just not possible unless you risk getting a fake ID.

No, of course the hotels need to know exactly who you are so if you destroy the room, leave a dead body behind, or steal all the towels, so they can charge your card or notify the authorities.  It flabbergasts me that anyone thinks they can check into a hotel anonymously?  On what planet did this ever happen?  

And no paying cash is not a good idea.  It's a red flag for illegal activity.  The hotel employees are trained to believe this.  Drug dealers, pimps, and hookers will be the most likely to try to pay in cash.  If your not doing anything illegal, why have any qualms about revealing your identity?  If you try to pay in cash, after the front desk clerk looks at you like your a law breaking mofo, most hotels ask for a $250+ cash deposit on top of the room charge that you have to go to the front desk and retrieve in person after they check the room to make sure you didn't trash it when you check out.  So if your only going to be in the room for a couple of hours, then that's going to again raise red flags when you check in and check out same day paying cash.  

Get a green dot, or a credit card that the SO doesn't know exists, suck it up and play by the rules like your not doing anything wrong because nowadays L E goes around to hotels training staff to watch for illegal activity to catch traffickers, pimps et cetera.  The more you try to get around this the more guilty you look.

you can reimburse her for the room along with the donation.

The best thing to do is have the PROVIDER book the room or only see providers who have private incalls...done deal. There is no rule that says YOU (the client) should have to book the room...most of us realize the need for discretion on your part, and are happy to book and pay for the accommodations in our name.

I'm there for P4P, I will mention that I will be paying with cash when I check out.  When I do checkout, I give them cash.

It won't show on your bill, but it will show if you log into your account online, until it passes. which is usually 10 days.