Analysis:

The HS-14 is a widened variant of the HS-12 with an added second stage. In this design, North Korea now has a real operational LRBM. It replaces the HS-13 project, which was probably discontinued due to problems with the Soviet 4D10 main engines.

So the speculation that the HS-14 is related to the HS-10 is nonsense. On the other hand, it is now sure  that the HS-14 has a larger diameter than the HS-12 (1.80m). The diameter of the second stage is 1.25m. Also sure is that it is a lightweight missile with tank framework.

The assumption, the first stage of the missile uses the recently tested engine (one combustor of RD-250) is probably true. The added steering engines comes from the HS-13 (R-27 origin). The takeoff thrust is approximately 464 kN. The first stage has reached an altitude of 585 km after 145sec burn time.

It was reported that the first stage of the HS-14 during a further launch in July had a longer burn time of 151 seconds due to increased fuel loading, and reached an altitude of 703 km.

The second stage is probably equipped with an engine of low thrust (4D10V?). The burn time of the stage varies between 225 and 235 sec depending on fuel loading.
The takeoff weight of the HS-14 is estimated at approximately 31 to 32 t.