@mczarnek - the biggest problem I see with your proposal as that each forger is being asked for a "random" number - how are you going to be sure of that?
I think that for the "ticket" (which currently is looking to be the forging hash of the block 1440 in the future) could have extra entropy by something more simple like the sum of the number of bytes in each of the 1440 blocks together with the # of transactions (and maybe several other such things so that trying to "construct a block" to benefit becomes so difficult it wouldn't be attempted).
I think also adding this amount of entropy helps because your ticket "isn't" just the forging hash (which could lead to people calling out *rigged* if a forger skips its turn).