Maybe need to look outside the box.
What's more important - keeping your 3 girls, or managing to get them served with the same breed?
My guess is you'd rather keep your cows and get them served with another breed, than get rid of them altogether.
Ever since I started with 2 herefords and used AI 3 times on one of them, and she still didn't get pregnant, I have used a bull.
I've bought a young bull, used him on my cows and sold him on at a profit. I actually use the bull for 2 years, sell him on as a still young, but proven bull and that more than pays for his overwintering, and saves a lot of time as the bull has never missed!
You don't even have to keep him long - just 6 weeks should be enough to guarantee pregnancy.
Or failing that - is there no one around that would let you run your cows with his for a few weeks, or even lend you a young bull? I've been quite happy to lend one of my young bulls out to an approved local home. Sometimes it can be advantageous to have them out of the way for a while so long as they are properly looked after and keep growing.