No- You do not need to disconnect the batteries to charge them up individually. Just make sure + and - are on the correct posts as you are hopping the clamps around.
Not sure a trickle charger will quite do it tho. 2~3A x 6 batteries will take a while.
When you have a bit of time (before closing the place) consider dismounting the charger off the car and taking the cover off the charger and having a look. In your off season you will need to bring something back to replace it. You need a plan. Either have this one repaired or update to a DQ.
We just went through two weeks ago.