Thanks again, everyone, for the info/discussion.

My mechanic came out this afternoon and took the battery and battery box
out of the airplane. There was some liquid on top of the battery and
inside the box, and a fair amount had drained out of the drain tube.

He removed the battery from the box, checked the levels and wiped it
off, washed the battery box with baking soda and water, dried it, and
took it with him to repaint the bottom inside. He also took the battery
to charge it on the bench and check it tomorrow. He said when you remove
water from an overfilled cell, you are also removing acid and changing
that balance which can also cause the overheating and boiling over.

He concurred with the person here that said the proper way to service
the battery is to remove it from the airplane, especially if it is in
the cockpit (like mine) vs. in the engine compartment. He also agreed
with the person that suggested that since my battery is in such an
inaccessible spot and I'm not a mechanic, a sealed battery would be a
good choice.

Thanks again for the discussion, everyone. Personally, I don't care if I
have to replace it more frequently, I'd rather have the sealed variety
that doesn't involve all this!

I am, however, still curious about the trickle charger. Is it
advantageous to have this plugged in between flights if you fly at least
once/week or is it actually detrimental to the life of the battery?