I have a sprint race coming up next weekend and its my first race that I would consider on a "hilly" course. Most of my races have been on rolling or pretty flat terrain so I just always rode my TT bike and never gave it a second thought.

Im a pretty big guy. I'm not the best climber, or the most confident descender(is that the right word?). I have heard this course described as, "if you aren't going up, then you are going down, there is no flat on the course." Its also followed up by a pretty hilly run course.
here is a map of the bike course https://ridewithgps.com/routes/2089497

here is the run course https://ridewithgps.com/routes/2089516

The course map shows 1200' of elevation over the 12 mile course. Followed by 300' on the 5k course.
My road bike is a trek domane with pretty relaxed geometry. 50/34 crank 11-28 cassette.
My tri bike is a fuji norcom 52/36 crank 11-28 cassette.

I'm leaning toward the road bike for a couple reasons.
The smaller ring on the crank should help me climb a little better.
I'll be more comfortable on the descents having my hands near the brakes.
More than likely I'll be up out of the aero bars on the climbs.

The only cons I can think of would be the geometry of the road bike. I cant really see any aero benefit over 12 miles. I guess my real question is, will the road bike kill my legs more for the run than it will help on the hills?
I'm sure I'm overthinking something here. I'm not fast, even on a flat road I ride 18-20mph. I normally run a 30 minute 5k.