Tri bike for sure, even with a disc if you have one. There's lots of little climbs in 112 miles, but not enough to use a road bike over a tri bike. When I lived in FL I did that climb in a few times in training for GFT and rode it 3 times in a row and the third time was in a 39-23 seated. Not real fast but it is doable. I'm too big to be a good climber. Take a day or two during your build up to ride the course or parts of it. It'll prepare you mentaly for that hill. It will not make or break your race, its a "blip" in 112 miles.
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Paul
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Paul