I think you miss the scale of strong storms. Updrafts and their corresponding downdrafts can commonly reach 40,000 feet with severe storms far higher than that. Many storms, especially in the central US can exceed 65MPH in forward ground motion.
I think you miss how high balloons can go. Strong storms top out at roughly 60,000 feet. Weather balloons can easily reach 100,000 feet and are often only altitude-limited by the fact that their skin is designed to burst after they reach a certain point. There's really no reason you couldn't design an airship for flight above storm conditions as long as its weight to lift ratio is kept low enough.
A balloon can be designed with excessive slack for accommodating the dramatic pressure differential between ground level and typical weather balloon altitudes, but neither airships (rigid or semi-rigid) nor blimps could ever hope to come close. Airships would fail to enclose enough volume power structural weight and blimps tailored for high altitude would fail to keep shape at lower altitudes.
Even if the problem was somehow solved for blimps, (perhaps with an internal "diving bladder" filled by compressing some of the carrying gas), their cross section at lower altitudes would be prohibitively big, making them effectively unmaneuverable. A very high altitude blimp would effectively be a one-way vehicle, it could raise as an uncontrolled balloon (then it might even be acceptable to not solve the slack issue at all), then operate as a dirigible at target altitude.
I fail to see why a blimp could not be designed in the same way as a weather balloon with a highly expandable skin. They already utilize bladders extensively. You would have to suspend your payload / drive unit below the balloon the same way a weather balloon does, but that's not a deal breaker. This seems like a materials engineering problem more than a design engineering one.
At launch, a high-altitude balloon is just a bubble of helium in a mostly-empty envelope. An airship with that much room for expansion would be enormous, even by the standards of airships.
In WW1, Germany flew some "height climber" zeppelins, which could reach 20,000 feet (still well within the range of stormy weather), but they could carry very little payload. They were also fragile, vulnerable to damage by quite ordinary weather. I think all other airships were limited to a few thousand feet, at least in practice.
