Skip the buckets of water; there is plenty of humidity in your area, even indoors, especially in a garage, unless you are going to blast dry hot air around in the winter.

A fan to create air movement and stir the plants a bit would help.

You have to have large grow lights to evenly light whole mature tomato plants, this could show up on your electric bill.

It does sound like a fun experiment.

I was thinking of replacing the old fluorescent fixture above the window with a hanging fluorescent (or LED) plant light, adjusting its height as needed. Many of the fluorescent fixtures are plug in, so an appliance timer could easily be added to the assembly. Thank you for suggesting ventilation--I would not have thought of it. A fan could likewise be on a timer.

Is pollination required? That's the one element I foresee that could monkey wrench this plan.

That's what the fan will accomplish. Tomatoes are wind pollinated. Or you can assist the process by jostling the plants gently when they are in bloom.

One oscillating fan to span the area could work, otherwise multiple static fans would be required. Creating a breeze can also help with foliage health and plant sturdiness.

Whitefly can be your worst enemy when you are growing tomatoes indoors. Strong oscillating fans and yellow stickem are used to combat them.
Mike

Yes: sucking bugs love it when you put host plants in hot and dry enclosed interiors, that's why parlor palms located in ordinary rooms (as opposed to greenhouses) always have mites and so on.