evolution - Is there theory that connects longevity, time-scale of environmental disturbance, and adaptation?

Not exactly matching your question, but I think that the idea (from stochastic demography) that life histories should be buffered against environmental variability in influential vital rates (Pfister, 1998, Morris & Doak, 2004) can be related to this issue, even if it is mainly (originally) dealing with stationary environmental fluctuations.

In general, fluctuations in vital rates cause the stochastic population growth rate to decrease. This can be described by Tuljapurkar's approximation (Tuljapurkar, 1982):

$$log \lambda_s = log \lambda_d - \frac {1}{2\lambda_d^2} \sum_{i,j} V(a_{ij})S^2_{ij}-\phi$$

where $\lambda_s$ is the stochastic growth rate, $\lambda_d$ is the deterministic growth rate based on average conditions, $V(a_{ij})$ is variance in vital rates (here matrix entires) and $S^2_{ij}$ is sensitivity in vital rates. $\phi$ represents covariances between rates, which can be important, but can sometimes be ignored for simplicity. This equation shows that the effect of variability in vital rates on stochastic growth rate (which can be interpreted as a measure of fitness) is a product of sensitivity to change and the amount of variability.

Because of the negative consequences on stochastic population growth, selection is expected to minimize variance in population growth rate. Pfister (1998) predicted (based on an evolutionary argument and the equation above) that a species should have smaller temporal variances in the life history traits it is most sensitive to. Therefore, across species, there should be a negative correlation between the sensitivity and the temporal variance of vital rates. This also means that the evolution of life histories and the tolerance of species to variability in environmental conditions are shaped by their life-history patterns.

A consequence of this is that in a long-lived species (as an example), you should find larger variabilty in juvenile survival than in adult survival, since population growth rate is more sensitive to variability in the latter. The lower variability in adult survival can then be seen as an expression of "hardiness" to variability in environmental conditions, and this theory can therefore be used to understand likely evolutionary trajectories of different species, also under a climate change scenario. The ways to minimize the negative effects of variability in population growth in this theory is to either be hardy in important traits (change in environmental conditions doesn't translate much into variability in vital rate) or to decrease the sensitivity in vital rates that vary a lot (which amounts to modifying the life-history pattern of the species). Your question mainly deals with longevity, and this is influenced by both maturation age and adult survival. Therefore, this theory can be useful to think about which species should develop a "hardy" strategy.

However, this answer completely ignores tipping-points in environmental tolerances, nonlinear responses and the genetic variation that selection can act on.

Related articles you might want to check out are Van de Pool et al (2010), Morris et al. (2008) and Doak et al 2005.