Haven't been in a Subway shop in years, but as I recall, the bread was "freshly baked" from frozen loafs, just out of the oven. Even the crappiest bread tastes good just out of the oven. Great bread tastes even better an hour or so later, somedays even a day or two later.
Is it possible that a lot of what you like about Subway bread is because it has just been baked.
The KA website has a recipe for Moomies rolls that makes the best bread for sandwiches, hot dogs, burgers, pulled pork, etc. Not sure if it is anything like what you're looking for.