I'd be curious to know whether you used the same method I did, or came up with something equivalent but simpler. The way I set it up:I am glad to see you revised your answer, because I got 171.5 (roughly), only 1 point away from perfect potential IIRC. I remember someone saying the math was hard... guess not LOL.
Divide attack rolls into three bins: outside the precision triggering range, inside the range with dice available, and inside the range with dice used up. Then assuming 69 attacks per day (20 rounds x 3 attacks/round + 3 action surges), divided in thirds between short rests, calculate the total damage for each possible distribution of 23 rolls into bins, and average, weighted by the probability of that allocation (the allocation is determined by the total number of rolls in the triggering range, which has a binomial distribution).