Just remember, power returns to source. If you create a parallel path between N and G, then G will have current.
You are referring to the Line terminal and it has voltage potential to the frame which is connected to G? It should have 120V AC, not 22V.
Positive/negative terminal is referred to with DC systems. So the question becomes, just what exactly are you measuring?
You need to use correct terminology in order to accurately discuss your "problem".
In order to give accurate advice, we need you to use correct terminology.
If you remove the grounding screw then how would ground fault detection occur?
N-G are bonded at the inverter under inverter power for the purpose of ground fault clearing, if there is a ground fault, then a breaker will trip.
The inverter model will work fine, you need to show a diagram on how you wired it. You could just have a defective battery or inverter, we don't know for certain if you are measuring AC or DC voltage potential.
Regarding a transfer switch, you would need to install a 3 pole double throw in order to switch neutral. This would be the same as installing a generator that has N-G bond.