The plan would be to have a total of 6 zones of light strips, 3 zones for under cabinet and 3 zones for over cabinet with a 100 Watt Class 2 DC driver installed in the sink cabinet to drive them.

Am I right in assuming I would first T the output from the driver into 2 zones for uppers and lowers and then further T those 2 zones 3 more times for a total of 6 zones?

If that is correct how do you split the wiring? Do you just use junction boxes and wire caps? Or, should I use a T-connector like the HADCO LCV4? They are a bit pricey but look convenient. I guess I should try to keep the wire distances and power requirements of each zone fairly equal?

Or, am I totally wrong about how to do this?

How much power do the strips require in total?
You can test out the setup with everything connected to make sure that the transformer does not buzz @ max power.

So, with those connectors do I push one set of wires into the input side and two sets on the output side? 16/2 AWG wire rated for in-wall OK?

Class 2 power supply means you don't need J boxes. This is similar to door bell wiring with power limited transformer.

Take a look at the following site. It would help in determining the gauge of wire and max length possible.
http://www.powerstream.com/Wire_Size.htm

You have to calculate the power consumption each run takes.

There is a voltage drop across the light bars. The max limit on the number of light bars that can be connected in series is typically stated by the manufacturer/ vendor.

Each zone would probably have to be wired in parallel not in series.