That barn looked pretty modern from the outside, if you ask me. There was even a nice silo right behind it. Artificial insemination is pretty advanced stuff, but on the other hand it doesn't require electronics or anything, so why not if he can make it work. A person with the power of a suitable law might be able to create liquid nitrogen for storing the stuff from a prize bull, but it wouldn't be economically possible, I guess. He might be able to do it locally if he had a rare slave knight with such a skill, but it would still do little for the whole nation.
As much as I like Liz, I'm still beginning to think Shingo should do something to keep her under control. While her jokes and plots are intelligent, they are hurting his job. He might want to consider sleeping in the same bed as her, for starters.