Danger, Will Robinson!
Some inexpensive battery powered square or modified square wave inverters connect their center tap to to ground (or indirectly to the battery ground and by design drive the "hot" and the "neutral" in opposite directions. Connecting neutral to ground on their output will either float the battery pack to 60V AC, it ungrounded, or let all the magic smoke out of the inverter.
By all means read the wiring instructions for the inverter.
Such inverters were once common in RVs and marine use and required a transfer switch that interrupted the neutral too when used with shore power.
The buzzing from the A/C is almost certainly the motor reacting to the square edges of the waveform and will probably correspond with a reduced motor life.
Inverters in RVs are not meant to run big loads with motors.
A 3000 watts inverter that derives power from a battery bank--can not support an A/C or even provide enough power to operate the unit for any discernible amount of time to offer comfort.
Have you tried running a small 5000 BTU A/C window unit with inverter using a battery?
Forget solar source with a miniscule power to even charge the battery bank to run the A/C.
My 13,500 BTU A/C unit won’t even start with the 3000W inverter.
For a 5000 BTU A/C unit, you can run it for about 3 minutes (if you’re lucky) and it will run down the battery in a hurry. It won’t even give you a chance to listen to the motor buzzing.
Forget the wave form of the inverter output.
Square wave or FAUX Sine Wave output-- won't save you--and allow you to run an AC unit with an inverter-- through a bank of batteries.
Location of neutral is irrelevant in the desired and expected operation of the inverter.
I run my 3000 W inverter only for powering my 32 inch TV and DVD player. (45 watts and 25 watts respectively)
It can only provide power to be able to watch one full length movie. After that one movie-- it will need help from the generator to recharge the batteries. . . but I have to wait.