JEDI, when used by McGuire aircraft, would be for a C-17A flown by a crew from the 514th AMW AFRC unit. It should have a two-digit suffix though.
Someone above mentioned F-22 types using it. True. Langley F-22A aircraft use it fairly regularly.
I also agree with the comment that it's unusual for C-17s to be using a UHF ATC freq. They certainly have the ability but it's just generally not done. That's the only thing that would make me question whether this was a C-17A you heard. Well, that and the 1 rather than 01 suffix.