Here's where I'm thinking about taking this:

1) Get some D-Latches working using sample and hold IC's.

Should be no sweat.

2) Test these out by making a variety of register and counter circuits with them.

This might be significantly harder.

3) Build and test a functioning Sum gate.

Tedious but doable.

4) Put registers and sum gates together to build a little state machine that calculates the fibonacci sequence up to 2 or 3 trits.

Hard.

The above would demonstrate a functioning truly ternary Class C machine. From my extensive research I couldn't find a single example of a true ternary machine of this complexity since they halted production of the Setun computers in 1965. The closest thing I've seen is a counting and adding machine that used two binary inputs per trit and produced ternary outputs. It was a nice demonstration of the logic, but wasn't truly ternary.