Time for an update! My system is complete and my plants (except for one) are planted. Everything seems to be in working order. The gist of the setup is this: a main water reservoir (33 gallon trash can) connected to an intermediate reservoir (small plastic storage box) with a mini-float, attached to the SWCs. The tubing that goes from the intermediate reservoir to the SWCs connects to the containers at the lowest possible point. It is important that the tubing remain below the water level at all times, or the water will not make its way through to the containers.
Here's a big picture of my setup:
Here you can see the connection from the main reservoir to the intermediate reservoir with the float, and then out to the SWCs:
This one shows the close-up view of the connection to an EarthTainer. The 1/4" poly tubing is simply inserted directly into a 1/4" rubber grommet. The grommets were purchased from a local hydroponics store for about $1 each. Each container also has an inline shut-off valve that services it, in case I ever want to take a container "offline" (these also cost about $1 each, or cheaper if purchased online):
Here you can see three 5-gallon buckets chained together (although one has a pepper plant, I couldn't think of any easy way to prevent back-flow and cross-watering between containers... we'll see what happens):
So, that's it. All of my tests so far have been successful. We'll see what happens when it gets hot and these plants start drinking! Thanks to everyone on this thread who offered their help and suggestions over the past two months!