iPhone won't latch on to LTE

Everyday as I get out of the subway it takes anywhere from 10 to 20 minutes for the iPhone to latch on to LTE. It remains until then in a state of disconnected limbo searching for connection - roaming in the cellular signal purgatory of  between 1x, Edge and 3G.

The only way to make it latch on to LTE reliably is either wait impatiently or to turn on and off Airport mode. Airport mode would be a grudgingly acceptable solution to me if switching it on also did not disconnect all bluetooth devices - specially wireless headphones. Disconnecting wireless headphones is so disruptive. 

ios 11 did nothing to fix this and I see zero chance of a new phone fixing this either.