Hi Patrick.
I don't consider myself a smart electrician. A smart electrician might advise you to consult with a state licensed electrical contractor instead of giving away free and possibly incorrect information over an internet forum but, if you cannot find such a contractor who has first hand experience with these types of RE inverters nothing has been gained so, I'd like to take a crack at it. I'll also give you links to the information I have found. As for telling you how to wire it all up, I will have to refrain from that because I cannot actually see for myself what you have. If I am right though, it should be fairly straight forward wiring.
You say there is a "neutral" wire coming from the pump motor? Is this what you see in the controll box?
http://www.do-it-yourself-pumps.com/franklin-electric-submersible-pump-control-boxes.htmThe explanation provided at the above site is somewhat confusing. It makes a reference to using a neutral wire with the incoming power but it tells us to land it with the EGC or grounding wire. This is pointless. The only time a neutral is needed is to obtain one or more single 120 volt line(s) from a 120/240 supply. The neutral provides a safe potential and can "carry back" the unbalanced load of multiwire branched circuits. When 240 volt alone is needed a single grounding wire is sufficient because the load is balanced against the two "hot legs" for the potential.
Are you sure its not a yellow "L2" wire? Anyway, it sounds as though it may be a simple capacitor start single phase 230 vac motor, only I would guess that the capacitor(s) is in the control box you mentioned. As opposed to being in or on the motor itself. What you are wanting to know is how to supply 3 wire, 230 vac to the controll box from a single inverter. Correct?
There is a single inverter capable of suppling 4 wire, 120/240 vac. Its the Magnum Energy MS-AE series inverter/charger.
!!CAUTION!! !!CAUTION!! !!CAUTION!! !!CAUTION!!
The wire coming from the pump motor that you are calling a "neutral" wire, may not be a neutral wire at all. Be sure you fully understand whats going on with this before appling power to the control box. Does the control box have a terminal for a neutral wire with the in coming power supply? Is there a neutral wire with the existing supply wires? If so, where is it landed?
Here is some more information about the subject from someone who has been in the business of RE water pumping a long time.
http://www.wholesalesolar.com/Information-SolarFolder/Invt-sizingforwellpump.htmlHeres is the Magnum MS-AE inverter/charger (24 vdc model)
http://www.wholesalesolar.com/products.folder/inverter-folder/magnum_ms_4024AE.htmlJust out of curiosity, would changing the pump be out of the question?