yes, you sure can use a general automotive charger like that one, put the charger across 2 at a time (2 in series for 12V) - a 12V battery is 6 cells in series, so 2 6V is still 6 cells in series.
You're more likely suffering from battery sulfation, so if you have one (a charger with a de-sulfation mode) use it - may require multiple cycles. The biggest killer of storage deep cycle batteries is using but neglecting IMMEDIATE recharge - sulfides occur when the state of discharge is left with out recharge. I use a lot of storage deep cycle batteries in marine use, and am adamant about recharge AS SOON as possible after use, and I've got grp31 batteries going on 5 years of service and still STRONG.
Some technical info, fully charge your cells, measure the open terminal voltage after they set for 30 minutes post charge (disconnect charger and everything else) and they should be roughly 6.3V per cell or better. also, on the charger, just prior to the charger finishing, they should measure about 6.9V to 7.2V per cell (what is called float/finish charge mode), when you first attach the charger after generous discharge, they may read as high as 7.7V or slightly more (what is called bulk charge mode). Hopefully your EZGo charger is a 'automatic multi-stage charger, if not you need to change out to one that is like what is used in the marine world, most are multi-bank of 12V, so you'd charge 1 pair of cells (12V pair) off of each bank. There are models that go as high as 20Amp per bank, which is generally adequate for those cells.