Round here (as in western CT), for what it's worth, a Reuben with pastrami is called a "pastrami Reuben," and seems at times to be more readily found than the corned beef variety. I think I've seen a Rachel billed as turkey with coleslaw, maybe? The terminology seems loose enough that I'm sure you could use it as a generic for "Reuben with alternate cold cuts" if you'd like to.

He informed me the inventor's privilege of naming was mine. I suggested Æthelred.

I'd vote for this. Some sandwich, somewhere in the world, in the world should definitely be called an Æthelred.

And then there could be a variant of the Æthelred, using slightly burnt cakes in place of bread, called the Ælfred. Perfect!