You are doing GREAT!!!!
The clipless pedals allow you to make very smooth circles with your pedaling motion. Most people who a standard platform tend to pedal "squares" or "stomp postholes" in their pedaling action. You want a light, fluid feel, a very circular motion, like an engine's crankshaft - it should spin, not bang around. High RPM is your friend, even if it's just the last few minutes of the bike portion before the run. Go into a lightly loaded high rpm and spin out those last few minutes (don't bounce on the saddle, stay smooth). It helps with the bicycle-legs that you get on transitions.
Tri-bikes are notoriously twitchy. They are often aero-framed or bladed-forks, darty in the cross-winds, very steep seat angle, and often the rider's weight is very forward. They are also the fastest bike out there for non-drafting events. Definitely need to ride/ride/ride one to keep from flailing around. Clipless pedals actually help when you are able to smooth the pedal stroke and LIFT (engage the hammies and hiney). If you can find a local school track that you can ride on, put the bike in the outside lane and ride it, keeping between the lines. Very safe way to smooth this out. Otherwise, find a quiet, long road with a little shoulder and a fogline. Ride just to one side of the fogline, eyes focused ahead, not down at the line, follow the line using your peripheral vision. You should be able to make pretty quick gains in this area.
I think you're training is really coming along. Working out with the tri-club is a great idea!! You are on your way!
angela