Help with Alternator Install

So... how about I connect the green wire to A and also make a jumper to ground B to the alternator body just to be safe?
Not needed. You are overthinking things.

Use a multimeter and measure resistance from B to the case of the alternator. Should read 0 ohms or real close to that.

And does any of that depend on which voltage regulator I have
If you have an electronic regulator like photo 2 in post 2 then you have the wrong alternator.

Post photo of your regulator