What you propose will work fine.
If it were me, I'd leave the injector side loose as you suggest (with a rag around it), zip tie or string tie or have a helper hold the shutoff lever on the pump up, and then bump the starter a few brief times. That'll bleed the line.
From there I'd release the shutoff, tighten the injector, clean up, and start it up. It'll easily take care of any remaining air itself.
I do not recommend holding the shutoff button down in place of mechanically holding the shutoff. Most/many of those shutoff solenoids only have the pull coil wired, not the hold co
So, if theybare held down for too long, they'll burn right out.
To bleed past the pump, you do need to turn the engine over -- you can't do that with the lifter or electric pump alone.
Have fun!
-Greg