I know Canada is the standard option for BA, but if it is your anniversary, how about a day or so in Bermuda, Bahamas or Mexico?

Take AA down there, enjoy the beach and then BA over.

Also, another option could be flying to Europe, say FRA or BRU and then use a LCC to EDI. I know, not as glamorous as flying to EDI in J, but as you probably know, intraeurope J is basically coach with the middle seat blocked.
You do get free drinks and meals in Y in Europe on a legacy carrier, so BRU EDI is very doable in coach.