I haven't done temperature tests on drums, but I don,t like the idea of a shaved drum on the West Coast. Hills in the Appalachians are often steeper than on the West Coast, but they are shorter (say 5-10 km max.), so the drum won't become too hot and will have time to cool down before the next hill. But when you face 15-25 km long downhills, you'd better have a brake that will cool down easily.

Drum vs disc ? The drum adds about 1.5 lb over the disc, and it's rotating weight. You will notice the difference if you lift it on your car and migt see it if you compete, but otherwise, I'm not sure. As to which one you need, it depends on your riding style, the roads you actually use and your desired margin of safety.

Some will say that unless you are heavyweights and/or pack lots of cargo, you could be OK with just the rim brakes if you enjoy high speed descents. If you prefer to ride at high speed and slow down drastically for each turn (or when it's too fast), then a rear disc is probably a better choice : you would "let go", then slow down with the rear disc before a curve, cattle guard, etc., and use also the front brake when additional braking is required.
On the other hand, if you prefer to slow down the bike all the time during a descent so it doesn't accellerate too quickly, than a drum brake is preferable. With the drum brake, you apply it moderately for a good portion of the downgrade (either with a brake lever as I do or with a shifter lever) to keep your speed at a steady 30-40 km/h, and you do additional braking before curves with the two rim brakes. If you have really bumpy roads or a nervous stoker – or if both of you weight 250-300 lb –, then the drum brake is the way to go.

Climbing gears ?
What gears does your wife has on her single? What are your climbing styles?
Assuming they are similar to yours and assuming you both have a similar climbing style, your suggeted 53-39-28 would work. Otherwise, you might try 53-39-26 or even 24, especially at the beginning.
If you are used to climb while standing on pedals, forget that for a while. You'll need to master your tandem skills and especially synchronise your climbing techniques before you stand.