Yes, the core successful behavioral response I see in my region to Varroa is nearly constant supersedure and swarming.
You see this in both AHB strains (which are present in my area) and in more nearly Italian hybrid mutts. I thought I had become a "god" of swarm traps, since I am so successful (after 10 years of false starts), but I think the arrival of AHB genetics has changed the bees to find my traps, and I am benefiting from the bees shift in behavior.
I've stated before I believe the maintenance of a highly selected and fragile genotype like Minnesota Hygenic is going to be impossible in the wild due to the constant "entropy" of a obligate outbreeding free-flying insect.
The simplest approach that adds fitness to the population is reversion to frequent swarming. Swarming has been selected against by breeders seeking to domesticate the bees as it reduces production and complicates management. The reversion to frequent and rapid colony division is an simple and robust reassertion of the feral genotype.
Swarming defeats Varroa by maintaining vigorous young queens uncontaminated with sublethal levels of virus. It provides a strategic broodbreak, and encourages new comb production. In my region, with its long summer drought and dearth, it is also going to encourage thrifty bees with small clusters. An "Italian-behavior" swarm in July is not going to enter winter in equilibrium -- too much brood and not enough winter stores.
A different climate (with a long, productive summer, instead of a drying one) might encourage a longer season of colony division.
In some ways, what I am seeing is the "Anti-Ives". The natural, successful wild colonies are small, compact young ones. Hiving these, and maintaining their ethology would encourage duplicating many nucs, single deeps or double mediums. Substituting colony numbers for towers.
Not much honey, but a king's ransom in pollination contracts (though you need to combine to make the contractual frame count).
The concept of local maximums of fitness and fragility of genotype can be illustrated. This concept has been explored for many organisms. Consider a hypothetical colony of F1 Minnesota Hybrids, these are wild-outbred, and might be at 75% on a scale of genotype "complexity". They have high "fitness" or say 50% of the colonies survive. Illustrated by the red dot. In future swarming, the sucessor colonies are going to reduce in complexity as they revert to the population norm (or 50% complexity where a minimum number of colonies survive). This reduces fitness. However, some local maximum of a very basic and robust genotype (say AHB) has higher fitness than the norm, and the meta-population genetics will gravitate to this easy to achieve (low slope to climb) local maximum. The movement to local maximums with intermediate fitness (sometimes quite low) is well documented in many species and in ecosystems. I believe we are seeing this in my local feral population, an all-purpose, not very productive, but highly robust social unit. The individual bees colonies sicken and die, but the meta-population survives by wild fecundity.
Remember when researchers fully described the honey bee genome, they were quite shocked to find immune response genes were deleted in comparison to other non-social insects. The evolutionary imperative toward simplicity and generalization, substituting social organization, has been operating on bees for a very long time.
Swarming could (and this is speculative) be controlled by a single gene expression of one component of Queen Mandibular Pheromone. QMP is well studied as a negative control on swarming, and is made up a collection relatively simple chemicals -- at least 3 very similar unbranched carbon chains. Minnesota Hygenic has been studied with "quantitative trait loci" and has identified (from memory here) 17 separate gene locations as central to behavior. This hypothetical difference (one gene coding for a QMP component) vs. multi-loci for hygenic explains the complexity of the genotype vector.