Your putting 30VAC into the regulator and only getting 2.2VDC out, that's not right.
Sounds like the regulator is not getting charge signal, battery is bad, or the regulator is bad.
Start by testing the battery voltage.
I don't think there is an electrical fuel shutoff on that model of pump.
There is a manual fuel shut off.
It's the red circled lever.
I would not try and start it or run it off of the onboard fuel system.
Use a remote fuel tank and feed the injection pump, just gravity feed it.
You will need to...
Yes it has float.
If it won't engage it probably has a detent section thats damaged.
Sadly the kit to fix it has been discontinued.
If you really need float your next option is to replace the valve with a newer model.
I have converted several B7100's to SSQA the are not out any further than my L.
Lift was as good as it should be.
You can get a lot more SSQA buckets for cheaper than you can mini's.
But to each their own have at it, will still beat the snot out of a pin on bucket.
Only other model of same generation BX1800
The BX2230 look to share the same parts
Go here and start comparing:
https://apps.kubotausa.com/illustrated-parts/
Give Oregon Fuel Injection a call and ask if they can test them.
Black smoke is almost always a injector or timing issue.
If you change the injectors you will need to have a dealer reprogram it to accept the new injectors.
You need to get better info, all the way around.
Adding anything to these engine to get them to fire is a huge DONT DO IT!
You very easily could have undone a rebuild.
If you had one injector "sticking it would still start.