UPDATE:
Well I lost lots of hryvni in taxi fares and lots of lost time.
1. I went to two separate Nova Poshta offices and was told the same: WE DO NOT SEND ANYTHING TO THE UNITED STATES. They send only to cities inside Ukraine and a couple of countries like Moldova.
2. On the internet it stated that there was a Meest office in this town. No one picked up at the telephone number listed. Took a taxi there, and it happened to be an Okko gas station. They had no idea about any Meest office.
3. The woman at Okko then gave me the address of a small Ukrpochta office in a nearby (smaller) town.
Got there. Office was closed. (It was around 2 pm).
4. Took the taxi back to the original Ukrpochta office. There was a different woman there, and she calmly started to process my order. Then another woman came by, Magda, an old acquaintance, and she starts loudly saying, "Oh, it's Sarah from Amerika".
So then the Bitch walked over and asked for my "dozvil" [authorization] for sending the books.
Back to Square One.5. I asked to see documentation that I could not send a 5 kilo package of 4 books to the US. She again starts talking about this little village "Velika Bakta" of 1,000 inhabitants where i need to go get the "dozvil".
Another woman comes out and shows me a book published in 2007 apparently saying that it is prohibited to send all printed material out of Ukraine.
They would not show me any documentation about this
Velika Bakta bullpoop.
So anyway, that is my experience. I'm in a small town outside of Uzhgorod. Those of you insisting to me that Nova Poshta sends internationally: maybe you are all in modern Kyiv, or maybe you really have not sent much overseas recently.
All I know is what you are telling me and what these people are telling me do not mesh, and it is frustrating as hell!

Sarah