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@gbj_tester
The physics doesn't really change much, regardless of the start and finish speeds or the time over which it happens. Because the inertia of the bike+rider is huge compared with that of the drive, the power needed to accelerate the whole plot is vast compared with the power needed to accelerate the drive components, so a small change in efficiency in the drive will correspondingly swamp any change in drive train inertia. With the whole drive train (ring+sprocket+chain) being about 0.5% of the system mass, and the rotation of the chain only about 0.05% of the eventual kinetic energy, it's just irrelevant.
Taking your jump, by the way, at the lower end of your example, accelerating from 20mph (9m/s) to 35mph (15m/s) in 2s needs 36W/kg plus aero and rolling drag. You can get about 15W/kg by dropping 3m from the top to the bottom of the track in those 2s, about half of which will be used just to maintain constant speed leaving the rider to find about 28W/kg to drive the acceleration. That's just about within the scope of elite track sprinters. 20mph to 40mph in 2s needs >50W/kg even after using the potential energy from dropping down the track.
On the rollers, assuming the usual cheating set up at Rollapaloser, the driven load is just a back wheel, tyre and a light roller, which only has about 25-50 (depending on the mass and geometry of the roller) times as much kinetic energy as the chain on its own, so the change from a very small drivetrain to a very big one could conceivably make a difference of 1-2% to the power required to accelerate, which is of the same order as efficiency difference during the 2s spin up. However, even if your small-ring drive gets you up to speed a couple of hundredths of a second sooner, you lose it all again in the subsequent 18s constant speed phase of the competition, where the higher efficiency big-ring drive wins.