I too would get rid of the alligator clips in favor of Anderson Power Pole connectors. You could also use MC4 connectors which are used extensively on large solar panels to connect them together.
There's no reason you can't charge your batteries with what you have if it keeps up with your needs. Sizing the solar array is more about how much power you're using than about how large your batteries are.
Either way, more solar is generally better than less.
You can certainly connect both solar "arrays" to one new charge controller.
200 watts will probably only do about 11 or 12 amps unless you get an MPPT controller. You're 10 amp would probably be big enough in all but the most ideal of situations where you had perfect, bright sun on cool panels. Do you know if it will just limit itself to 10 amps or will the extra power burn it up?