How to determine the evolution of a dimension of fitness that has high variability of selection intensity?
It's complicated. The classic answer is from Dempster 1955 Cold Spring Harb Symp Quant Biol 1955. 20: 25-32 (doi:10.1101/SQB.1955.020.01.005), which has a whole section on "Selection Intensity Varying With Time".  Summarizing:


An example from Kimura (1954) with a mean selective coefficient of zero: "the variation of selection facilitates the loss or near loss of alleles thus tending, if anything, to decrease rather than maintain genetic heterogeneity".
An example with haploid populations (approximately equal to the diploid case for weak selection) with a time-varying selection coefficient of $s_k$ shows that the behaviour of allele frequencies over time depends on the mean value of $m=\left\langle x_k \right\rangle= \left\langle\ln(1/(1-s_k) \right\rangle$, i.e. the geometric mean of the relative fitness; in general, the geometric mean is smaller than the arithmetic mean (i.e. variation in time would lower the fitness advantage of the more-fit allele). I believe the bottom line here (although it takes quite a bit of work to understand the whole story) is as given in the last sentence of the paper: "Selection pressures variable in space or time could act to maintain genetic variance of fitness ..."


On the other hand, Tănase-Nicola and Nemenman (2011), "Fitness in time-dependent environments includes a geometric phase contribution" (DOI: 10.1098/rsif.2011.0695) say it's still more complex:


  the selection coefficient in infinitely slowly changing environments (we call this the adiabatic limit) is given by a time-average of static selection coefficients corresponding to each environment. This time-average is equivalent to the geometric mean result of Dempster [10]. It is independent of the order or the speed with which different environmental states are visited. However, for environments varying at a slow but finite rate, this time-average is not the whole story ...


All of the above is about the evolutionary dynamics of a single allele, not a comparison of the evolution multiple alleles/traits within the same genome.  Things could get (much) more complicated in that case, even in the absence of explicit pleiotropy, linkage, etc. (e.g the Hill-Robertson effect). I doubt there's a simple answer; I would suggest heuristic guesses based on independent dynamics of alleles based on the single-allele phenomena described above, followed by simulation ...