Surely temperatures are not an issue this time of the year for you. Can you grow your basil outdoors?

FataMorgana

"They're so leggy that I would prefer to cut them all the way down. Why would a grow light seem to make them worse?"

Leggy means not enough light. Grow lights need to be on 14 to 18 hours a day. I have mine on a timer and they turn off for 6 hours at night. Check this out (copy & paste into browser url).

http://www.waynesthisandthat.com/fluorescent.html

The plants need to be as close as possible to the fluorescent light source to maximize light intensity, within a couple inches!

I also set the plants outside in direct sun, when weather permits, starting at a young age. So far, this seems to help reduce transplant shock (sun scald, wind damage) when moving them outside for the summer.

I'm in zone 5. I have no zone 10 experience.

With the grow light it's possible that it's not being run for enough time during the day, or it's not strong enough which could be the problem with cheap fluorescent. I'm guessing your grow light is fluorescent. It will flower eventually, especially since fluorescent is spread spectrum. If you had less red wavelengths the plant would not flower.

Since it's already flowered the taste of the herb will start to change. It may be best to start over or experiment with this one.

Here is a link that might be useful: Artificial Lighting for Growing Basil

Claydirt, have you considered further testing to see if the aquarium lights degrade anymore after 6 months? If they're holding their own at months 5 and 6 with a 10% reduction in output, perhaps they'll hold it a little longer, and make swapping the bulbs out a month or two later?

You need to leave a few leaves on top for photosynthethesis. I would keep them misted daily. As soon as you can get them outside the better!

Only the top leaves of any plant will benefit from artificial light, plain fluorescent or grow light, doesn't matter. And with basil, as an annual with a finite life cycle, I feel that once it has persistently begun to bolt (which it will do if stressed for whatever reason--including lack of sufficient light) you have lost the battle! Basically, all it is striving to do at this point is set seed in order to ensure the survival of the species!
Also, since the leaves are are yellowing, I am surmising a nutrient deficiency. I'd suggest you start new plants, and if you simply cannot grow them outdoors (really? in CA??) at least try a dwarf species more suitable to a container such as Spicy Globe.
Get a good organic fertilizer --maybe Sea Magic or Neptune's Harvest, maybe add some worm compost to the soilless mix you are using. Just don't try to plant in regular garden soil or commercial potting soil with fertilizer added. Potting soil is too heavy. Use something labeled seed starter, then add your own nutrients as suggested. Or if you must use potting soil, mix it half & half with perlite and maybe even some vermiculite also to lighten it up and make it drain better.

The good thing: you are correct in not overwatering!
Good luck.