I went back and reviewed parts of it also. Subsection 61.31 is the central (maybe only) issue for discussion. The main reason I can see that helps support the proposition (making the mistake of thinking logically while approaching a bureaucratic monolith) is that both aircraft under consideration are usually under 12.5 gross and even in the heavier variants of these two the weight over 12.5, while significant, is not out of the realm of "normal piloting skill" (made up phrase). The -300 Twin Otter is one of the Ikhana increased GW STC while the Beech is a production variant of the 200/250. The limited amount of time needed, 1-2 months, may also help the argument.
Beyond this is still the issue of what Part the aircraft would operate under. It is "for hire" but not as a revenue passenger vehicle. It will carry two equipment operators but can they be considered "crew", etc.? Both company pilos are commercial and IFR licensed and otherwise qualified to fly complex King Airs except for currency checks. And, further, whose ticket do you use - the lessor or lessee? This is one of those exercises that if it doen't start getting a little easier as you dig deeper it is likely to fail especially if there is a time factor. Still, as you said, it will be interesting to see what they say. I've already called them and waiting for the call back.