To say LAM not on our route, where would you like after there? until you are given a point on your route. A controller should not issue a point off your route unless they have a good reason for it, and I would always say in your example route LAM DET.
We seem to be in violent agreement there then, 5milesbaby.
By the time you have realised and selected 7600 you may be off route by a massive distance, so if going to DET or LYD makes more sense than going back to BKY then do that. Again, we'll see the squalk and will be clearing EVERY a/c within reasonable distance both above and below right out of the way so that whatever you do is covered.
Wouldn't it be easier to share the plan with the pilot, though? I know there are moments or even minutes of high intensity RT, but it only takes a few words to create a default route for comm failure purposes.