Hope things work for you. As I understand it, some mulberry varieties root readily and others are very difficult. I tried two varieties in a misting chamber last year and had zero luck. Report back if you make progress!
I got some wild female mulberry to root last year, although not much growth, they are alive, I dipped in root hormone and stuck a bunch into a 3 gal pot, just stuck it in my nursery and watered them when I watered everything else.