Wouldn't have harmed BT if they at the outset proportioned the LRS to what was left of the annual contract so that it all synced, after all they do something similar on the monthly quarterly charges when you change packages.
It's not in BT's interests for a customer to have all their contracts, and LRS, in sync with each other. They are happiest if the customer is locked into an endlessly rolling series of overlapping contracts, such that they would lose money whenever they tried to leave.
It's up to the customer to prevent that happening, even if it means paying a bit more than necessary for a few months until it all lines up. Once the final contract is about to expire, that's when you look around at the competitors' prices, then phone BT for a better deal.