Well, initially I thought B-F might use its own rye (made in KY) and apply the Lincoln County Process in Tennessee to lend a distinctive TN note. This is why in my earlier post I said, "or B-F might put out its own rye", i.e., do an all-Kentucky rye as an alternative to any such use of rye at Lynchburg although I suppose it could be both (but not as likely IMO).
Giving it further thought, I think if JD or GD ever did a rye of their own they would probably make it from scratch themselves, 100% in TN. Being long-established and with the Tennessee origins long a point for distinction for them, it is probably unlikely they would bring in rye for this purpose although as a niche product, who knows..?
Either way I'd like to them do this and B-F too to put out its own (non-JD named) all-Kentucky rye, the more the better.