The model I've proposed above for the probability of exceeding Jack's jackpot is obviously unsatifying since it pretends that 6 linearly increasing jackpots would occur, whereas it is more likely that some kind of lotto fever will click in and result in non-linearity.
Of course the difficulty is that we are in new territory with the new Powerball odds, so we cannot really look at the past to model prospective futures.
However I did think of a model that is slightly more satisfying. The most recent case of lotto fever was the recent Megamillions run which went up to $250M annuity. This is the only super high jackpot of the super high odds era. Graphing the sales of this run shows the slope of the line increased radically for the last three drawings, indicating some level of lotto fever.
The sales were not, of course, evenly distributed. The first of the three rollovers accounted for 24% of the surge towards the final jackpot, the second, 31%, and the last, 44%.
To beat Jack, the cash jackpot would have to rise about $70 million, requiring $240M in sales. If the distributions were the same in Powerball as in MM's last three in the lotto fever run, the sales would need to be respectively $57M, $75M and $108M.
Estimating the odds on three jackpots of these types gives a 40% chance of matching Jack's pot, and a roughly 20% chance of going beyond Jack's pot with an additional rollover.