which bike to ride

Address WHY you're not as comfortable on the tri bike in those situations. Is it a mental thing? Is it because your hands aren't on the brake levers? Is "too fast" the same on both bikes?

Staying in aero isn't necessarily always the fastest. I've put my hands out on the base and can then drop my torso even lower. Also make sure to keep elbows tucked in. Might be able to go faster like this. For the gear, I'll pop it into a big one and just leave it there. I can pedal a wider cadence well enough and know I won't be putting out lots of power when going faster as it doesn't really gain a whole lot.

Getting used to the grip and feel can take some practice. Different bars can do this better than others too. Even with a slight bend at the front, they usually don't inspire as much confidence as the roadie drop bars do. There is also getting used to the feel of the turn. Decent road bikes can feel like they're really meant to be thrown over into a hard turn. Tri bikes are meant to go straighter and can feel a little funnier when trying to corner hard. It's in the steering geometry and weight balance where they'll do good for tracking straight, but then may seem twitchier if you try to lean over farther and faster. It takes some practice to get used to.

I'm faster climbing with the tri bike than road, so have been ok there. I'm not sure why some people are slower, but it does seem to happen. Mine haven't really been heavier, have definitely been more aero, and can put out power just as well in them.

Is this a point to point course with only one descent?

Just doing the math, if it's two 1700' climbs, over 17 miles, and is net elevation gain of 0, then even if there is no flat riding, you are either going up or down a 7.5% grade.  3400' total climbing, 8.5 miles of uphill, 8.5 miles of downhill.

If that were the case, I'd probably use a rode bike as my tt bike is not fit with the bull horns in an ideal climbing position.  I'm certainly not going to be climbing a 7.5% grade on the aerobars.  Even for the downhills, I rather descend a 7.5% grade on a road bike.  You don't even have to worry about pedaling at that steep a descent, so it's all about getting lower and having confidence braking and turning.  As Ben mentioned above, you can likely get lower on a road bike assuming you don't have to pedal.

If there are any flat portions on the course...then the average grade climbing and descending is steeper.  If it is a point to point net elevation gain, then it depends I guess.

That part was actually entirely about the tri bike. Getting lower when out on the base bar/horns might be faster than staying on the aero bars. In comparison to a road bike, I don't know. I've been faster on tri bike here too though lots of people who know what they're talking about can get a lot of speed on the road bike as well. Especially getting into a pro level tuck (that I doubt Stuart is going to do ).

I've taken the road bike up to hilly areas after being on the tri bike for awhile and didn't descend any faster in the turns. There was just too much shadow camouflage in sections and the turns themselves were quite blind on narrow-ish roads with a very real chance of gravel and sand coverage just around the corner. This is not to say one bike or the other, but thinking things through as answers may be different for various reasons.

Sometimes it helps to look more directly at the route & profile.

ETA: Event website

Thanks! Hadn't thought to look at the HITS course too. From what I can see, that looks more relaxed then the craziness some of us may have been thinking. The overall grade is still low (under 2%) even though spots may be quicker. People should still use aero quite a bit going up. Coming down, it'll help boost the speed certainly, but also doesn't look like a crazy roller coaster ride. That top mile looks the most interesting. Keep working on getting more comfortable with the various suggestions and see how you feel. A December race is still quite a ways off.

Also, if you look at the KOM for the descent, the guy - a Canadian of course  - never exceeded 40 mph yet was putting out 260w on a decked out P5.