Been somewhere similar, faced something similar, wish I could have gotten a t-shirt out of the deal...

It boiled down to "play her game or live my life" for me.

If she needs to be coy and send certified letters to someone she speaks to on the phone to fully engage in her world, and if you want to engage with her within her world, then take time off work and go get the letter.

If you'd rather live in your world and make her engage with you in it, then don't. You already talk on the phone, so it's not like you are cutting off communication.

Whose mental health do you want to nourish? If hers is a special project for you, devote yourself to it. If your health is your project, don't work within a convoluted mindset with someone whose goals may be very different than your own.

(And don't forget the legal aspect. If there is some legal issue waiting in that letter, it could get ugly.)

Good luck. Remember what they say in the airplane safety demo: put your own oxygen mask on first, then assist those around you. You are useless at helping anyone if you yourself are already suffocating.

It's harsh, but sometimes we are forced to make these choices.