Just brainstorming here, could you possibly approach risk of an option from a probabilistic perspective?
Because the price of the option ($S - X$, where $S$ is lognormally distributed) is lognormally distributed with the same standard deviation as $S$ (aside from being truncated at 0 and having the probability go to infinity as $S$ decreases or $X$ increases, which would pose issues) we can assume that the volatility of the distribution of $P$ is most sensitive to changes in $\sigma_S$, not $S$. Therefore, based on the historical distribution of $\sigma_S$, could you not compute the implied distribution of values of the price of the option?
Essentially run a low-iteration Monte Carlo sampling from the historical distribution of volatility, then use the output of option prices to estimate a distribution of returns for $P$, and therefore the risk. Just find the optimal volatility by running volatility for different periods and finding which one most closely matches the current implied vol.
I understand that the math to support this is completely absent and there is likely a huge flaw in the assumptions made, but it may be a solution. Just choose a holding period and only calculate for that one $t$, or iterate across all $t$ and have a dynamic volatility that would require automatic rebalancing.