I would say the decision to ride something as beefy as gatorskins is more of a choice than a necessity on tandems. A lot of people really want to avoid flats, but if that's not an overriding priority for you, then you don't need to go with something that chunky.
We (about 330 lbs with a racing background) generally ride tires as wide as (1) fit the tandem and (2) are very high quality and supple and so get good performance out of them. The move to wide tires on road bikes has helped in this regard as you can now get top quality racing tires, e.g. Conti 5000s, in 32 wide, which at one point you would have struggled to find them in wider than 25. The Vittorias you mention are a pretty nice blend of durability and suppleness, and, since you have them, I would certainly try them out and see what you think. At your weight, the 70 psi on 35s should be fine, though you could overinflate somewhat as well.