Can the BL5340 or BL65x use a different stack to support a hosted application?
Theoretically as long as whoever 3rd party BLE stack is used is tested and supported on Nordic nRF5340 or nRF528xx used on BL65x modules.
Laird would not have tested anything other than Zepher/nRF SDK.
A 3rd party CODEC could be used as well as long as it is targeted for nRF5340. However, licensing would need to be considered.