I can see what your trying to do..... and I have sad news...... not usefully practical.
You have an induction single phase motor. It's peak current will be 3-4 times run current. So you need a decent inverter to start it reliably.
It also means constant speed ( will follow frequency not voltage) so you cant turn it down ... all or nothing.
This means as you say batteries, which loses a lot of efficiency. It is a KWH game you need to put the KWH into the batteries first, then pump for 1/4 of that time, and charge again. (remember chemical losses). Even full solar while running will only delay the discharge cycle by 1/3rd.
Even if you could slow the motor (variable freq drive?) the chances are that they use a stacked rotor design, rather than a helical design (better but not as popular for some reason).
If this is down a well, where you can't use a surface pump, then you really need this:
http://www.ebay.com.au/itm/500W-48V-S-S-SOLAR-BORE-PUMP-SYSTEM-2-YR-WARRANTY-/190548812134?pt=AU_Pumps&hash=item2c5d982166 No batteries, helical pump ( virtually full pressure at any rpm... well almost... not like a stacked rotor) mppt built in for only a grand.
Trying to save by making use of the current pumps will cost lots more (batteries and controllers and 30% less efficient).
I recently built a solar pumping system for over 70m head >60 lts/min... over 38000lts/day in summer (easy).... but we were pumping from a dam, and so used a helical pump driven by a standard 3hp DC motor with a modified curtis golf cart controller(260A @ 36v.... no batteries )
It. works very well, but we didn't have to draw the water up more than 12 feet..... then up pushed it another 200 feet up and a few kilometers away.
If your pumping from a dam, then this could be a way to go for you too.... but helical pumps are expensive things (our pump was a standard AGP520 Mono... $1800 just for that.... ( we can belt drive it from a diesel next to the electric motor ( swap belts) and pull easily over 120 l/min into 80m head.... it is a big pump).
Single phase induction motors work very well and simply on the mains.......any where else they become a problem with surge and the all or nothing speed thing. You cant reasonably back them off when the sun fades out.... even if you had 2000w solar. Three phase you could do much more easily.
................oztules