How would a low-airspeed fixed-wing drone be designed to reduce effects from gusts and wind shear?
First, kudos for the well-researched question! You certainly did your homework before coming here.

As you realized yourself, your requirement is quite contradictory. I also wonder what blimp would be flown into hurricanes, but I leave that aside for the moment.

In order to reduce gust susceptibility, a variable configuration would be one option. However, just when you want steady flight in gusty conditions, you also will fly slowly, so variable wing sweep or elaborate wing flaps will not help. The next option which combines low flight speed and high wing loading would be some direct lift, like in the VTOL-designs of the 1960s. Since the direct lift is needed for a short time and when propulsive demands are low, an engine like the Rolls-Royce Pegasus would allow to add lift that is less affected by gusts than the wing.

Make sure your design will draw ample bleed air in order to feed the reaction control system, and maybe a gyro platform to control this system, and the contradiction can be resolved.

Stalls should now be less of a concern, too. Much of how much lift is lost in a stall depends on the choice of airfoils, and if you use one with benign stall characteristics, stalls can be tolerated.

Anhedral is a poor idea, however, especially if you use unswept wings. Only if you have a high wing on a large fuselage can anhedral be justified. Examples are the Harrier jump jet and the F-104 Starfighter, where the large T-tail made wing anhedral necessary. You want moderate dihedral in order to make the aircraft roll in a sideslip. This rolling motion will tilt the lift vector sideways and pull the aircraft away from the sideslip condition.

Also, please reconsider whether there really is such a thing as a pendulum effect.

Regarding the tail: The best one is as symmetrical as practical.