I agree with RobertC. Starting and stopping charge like that isn't good on the charger and relays/contactors. Plus, It'll take 40+ hours to charge the car if you don't run the forklift battery flat first. Remember, also, that if you have 500 watts of incoming solar power, you can charge at 1,000 watts and the battery will still only see a 500 watt load.
Forklift batteries are designed to discharge up to 1,400 watts. Your best bet is to have the cord upgraded by the way of EVSEUpgrade (if you're in US or Canada), and set it for 6 amps at 120 volts, which will be around 660 watts (car stays about 1/2 an amp below the EVSE pilot signal).