Thanks for all info guys.
Attic space is one and a half stories up, well ventilated above and below, unheated, unfinished, in climate where it gets really hot and humid, and where the sun will beat directly against the siding 6 hours a day, till the sun suddenly sets.
My local supply store only has Johns Mansville, Foil faced, foam insulation sheathing, half-inch, four ft by eight ft. I'm going to go with this, with the foil facing outward, so it is directly against the back of the T-111 sheathing. I will nail it to the studs first, and then the T-111.
Happily, this is only a small area of siding, about 3 ft by 14 ft, so I don't have to make a decision for the whole house!
Thanks again,
Mannyrock