Another plug here for the morningstar mppt 15. I use this with a 260 watt panel, very similar spec to what you've shown. I originally contacted morningstar with similar worry about going over the limit on the amperage, answer was it will charge at 15 amps max, controller doesn't use the rest and will be fine. No problems in several years of use now.
To connect you'll also need to buy the USB meterbus adapter and download their msview software, then you'll be able to match the setpoints and timings (among a bunch of other settings, its pretty configurable) to the exact spec of your batteries if you so choose.