Any recommendations for giving gifts that don't happen to coincide with a meeting with a provider, such as for a birthday or other occasion?  Depending on the privacy constraints of the provider, I assume that mailing something physical (lingerie, jewelry, etc) would be untenable, as it requires a physical address.  And Amazon gift cards are impersonal, despite being practical.  Is there anything better that protects a provider's privacy, or is there a solution to the mailing address problem

See if the lady  in question has a wish list on her website, if she has one on Amazon, as a LOT do, you can send her something from that without you ever seeing her address.  

If she doesn't have a gift list then you could get her a gift card to email. You could choose something that she's interested in, or based on conversations you've had to make it more meaningful. Pilates studios, lingerie, opera tickets....  

repeat visit. Both of you will enjoy immensely.

so simply ask the girl.