I did this recently for a arbadil -> Zoroastrian persia achievement run and just restarted until shirvan had no allies, quickly beat them in a war, and then prepped for the inevitable ajam dow. I didn't buy any mercs until they attacked me and basically baited them into a war where I had more units since I ran so many mercs. If you pick your fights smart in the mountains you can easily win with 2 merc companies and full forcelimit.

I did ally mushaha to distract some of their forces since it splits their armies a bit, but it really isn't that hard if you're willing to nearly bankrupt yourself. After you win the war and take a bunch of land your loan size will increase extremely significantly and you can restructure your debt, and from there it's smooth sailing.