Really Cinno, you may have a good understanding of physics principles but you set up this problem with the wrong assumption that the track is coupled to snow and no slip is occurring. Your logic may be true if you're ripping across a lake at 60 and punch it, but not from a dead stop in deep snow.
In reality, the sled moves forward because of the amount of snow the track is propelling backward. The more snow thrown by the track, the faster the sled will move. So the faster the track accelerates, the better and more responsive the throttle will feel.
Its easier to discuss the rotating mass issue by itself by setting other variables constant (traction). Once that is settled we can move on. Shall we? OK.
Your statement "In reality, the sled moves forward because of the amount of snow the track is propelling backward. The more snow thrown by the track, the faster the sled will move". It sounds like your saying its "jet thrust" like water through a nozzle. I don't believe that. I would simply set the traction coefficient somewhere between 0 to 1. 0 = no traction and 1 = maximum traction. Maximum traction couples all the force from the track to the snow. The sleds reflected inertia to the motor is rotating inertia of all the drive train components plus a portion of the total weight of the sled based on the traction coefficient. So the effect of a 5 pound reduction in track weight maybe "felt" by the rider if the traction coefficient drops significantly . So you get that zippy feeling in soft fluffy snow, lower lug heights, shorter length tracks. SO the math proves it! Can we be friends again?
So my opinions on track selection. longer, taller lug tracks are heavier so you give up inertia to gain traction. However increasing the pitch reduces weight so you get back a little zippiness without giving up traction. Some believe the longer pitch reduces the fracturing of the snow which gives better traction.
Another thing when Polaris raises the gear ratio on longer length and taller lug tracks the reflected inertia drops even though the tracks are heavier because of the 1/gear ratio squared function. Any comments from those that have changed ratios without changing the tracks and how that effects the zippiness?
Cinno