I'm really curious about the bike calculations. Riders who stay on their TT bikes will benefit from decreased wind resistance even on the hill, but riders who change to their road bike will benefit from a lighter weight bike. Which saves more time?
On a 6-minute steep climb, assuming road bike is 2 kilo lighter, one could gain around a dozen or so seconds (so not much more than a time loss due to a bike change). This is a simplified assumption cause:
1) Gravity isn't the only resistive force to overcome - on a steep climb it's a large majority but not all (the remaining force will be smaller with a TT bike)
2) Power output may vary on TT bike (vs road bike) with possible advantage of the latter.
Those two factors have opposite influence which makes things more difficult plus there's a shallower section also (which alone can actually make very little difference due to moderate gradient ).