Thank you for the post. While I think building mitigation based on the damage ratios you calculated in the chart will definitely be an improvement over 0th order approximations such as stacking only physical damage, or maximizing total unweighted sums of mitigations, I'd like to offer two potential 2nd order corrections to the above post, for the sake of discussion. Do note however that I am not a tank and all the arguments below are qualitative and based on intuitions. Quantitatively I'm not sure how big of an effect they have, and thus how worthy they are to be addressed. So I'd appreciate insight from you.

Firstly, the weighted sums of damage taken considered, at least after the tanks have a mature build and won't die easily (and probably after distributing their mitigations based on your calculation), should instead be based on windows right before they die and when they nearly die. This is a point beyond the purpose of your post, which is a general improvement over unspecific stacking of mitigation. But I just wanted to put it out there.
Essentially, for built/established tanks, my guess is that deaths are usually due to accidents such as pulling too many mobs at once, or fighting in an area where mobs respawn. The former is due to the inherent structure of the map, while the latter might also be due to the paths the tank/leader is taking (which probably forms a somewhat consistent pattern). As you mentioned, this is when any data such as combat logs will be useful. But even without it, one way to tackle this might just be to do a test run with one's common party in the map, pin down locations and frequencies of deaths, and do the weighted sum based on mobs in those locations.

Second, even given a table of mobs whose damage mitigation is to be optimized (either across all elite mobs in the map or based on my first point), several temporal effects are to be considered that might favor stacking physical mitigation over other types of damage (such as fire), at least for a sufficiently coordinated party. In particular, in your post the assumption of random and uniform damage could be the first to be loosened and extended. If the party is able to focus down the fire damage dealing mobs, as well as using rage controls and stuns on them (which should be quite easy to remember, the mage-luts and the overseers are clearly fire-damage dealing etc..), then that'd apply a primacy-bias like filter to the damage taken, such that the fire damage taken is even less than average.
In addition, active mitigation abilities like shield's elemental ward, where the defensibility is strong but only available over a limited window, should be more effective than its % up-time (e.g. 33%). In fact, this should be the minimal performance of such active mitigation skills, considering any damage patterns deviating from entirely uniform/random means there are time windows where the damage within exceeds 33%. (I actually wasn't sure why you said it'd be slightly less than that - are you referring to effects such as cast times? - and would appreciate clarifications.) The point here is that mobs usually have several typical ways of popping up (based on my limited experience). Either they just all come together, in which case the damage taken is highest at the beginning and monotonically decreasing. In such case, poping the fire shield at the beginning and focusing down any fire mobs will largely reduce such damage. Alternatively, If the mobs instead come at separate waves, then trying to maximally the overlap between them might be the way to go. This is of course assuming ~10s is enough to focus mobs down. But so long as it takes less than 30s to do so, then this is something that can be leveraged. Instead with the majority of elite mobs (11/16) dealing physical damage, it is relatively preferable to have physical mitigation being passive. Obviously, this point does not apply to skills without active mitigations (and I don't really know how many skill combos can work for tank, and how many of them have/don't have active mitigations), but based on a quick search of what you listed, seems like quite a few of them should take this into consideration (such as shield, deer, staff, and unarmed, iirc).
Finally, I'd like to reiterate that this whole 2nd point should be considered as a perturbation from the mitigation ratio established from the table, constructed based on your post, instead of a point arguing against it.