How to calculate wattage used in a solar panel set-up
I’ve not seen a golf cart battery that was only 20AH , the 215 number sounds plausible so you would have 215 Ah at 12v with 2 batteries. 

Are you sure you have your numbers correct? My guess would be you have an inverter that outputs 300w at 120, to do this it would draw ~25 amps from the batteries (the draw would be more because of losses in converting 12vdc to 120v ac). 

If you want your batteries to last don’t discharge past 50% but golf cart batteries “deep cycle “ can go down to 80% but will only last a couple of years.
 Using 50% this would provide around 4.3 hours of run time from the batteries alone 25amps or 107.5 ah used , your run time would be extended by adding the solar if in full sun your total run time could be 11.8 hours as you would only be drawing ~9 amps from the batteries but you know your not going to have full sun and this would leave the batteries in a depleted condition or at 50%. 
If you provide more information on your inverter we may be able to provide better examples.