I understand you are looking to the second term of API formula.
I think your problem hasn’t a simple answer- and for this fact API doesn’t enter in details.

Let’s simplify the discussion looking to a "dummy "fluid mechanics model.
One pipe is connected to a large vessel and the other end of a pipe exits into the atmosphere.
The vessel is large enough so even in steady-state flow the vessel pressure ("large enough") remains constant.
So the pipe is connected to an "infinite source" with density0, p0 ,T0 and discharge into atmosphere with p_atm. T_atm. The pipe is adiabatic insulated.

There is a steady-state flow trough the pipe. At the endpoint, the gas pressure cannot drop to match the atmospheric pressure without the gas accelerating to critical conditions. A shock wave forms at the end of the pipe, resulting in a pressure discontinuity. In my opinion that discontinuity results in energy dissipated in the atmospheric turbulence so the pressure that would be taken into consideration in API reactive force formula is the "upstream shock" static pressure. This approach would be questionable but anyway is conservative.

It is true also that, the choked flow at the endpoint can be count as Laval. However it is difficult to apply these equations to choked conditions, because the local conditions upstream are not known at the point of choking.
Anyway, to perform this calculation, one must be able to calculate the stagnation pressure and temperature at the end of the pipe, upstream of the shock wave. How?

The real behavior of gas flow in adiabatic pipe is the gas accelerates along the length of the pipe. As the pressure drops, the gas density will also drop and the dropping density must be balanced by an increase in velocity to maintain mass balance. So to make a calculation means to evaluate pressure, temperature and gas density as "local conditions" upstream of the shock wave. In this case, important is to simulate the flow trough the pipe.
Even so, the fluid mechanics model is a little bit strange since you know one boundary condition at the end of the pipe (Mach=1).
BTW, if you take a look in the section "Discussions" of the famous article "Steam Flow Through Safety valve Vent Pipes" by Brandmayer and Knebel, Mr. G.S.Liao said "In any case, the conditions at the vent pipe inlet can not be determined without knowing the conditions at the vent pipe outlet. Therefore, the calculations are always backward". True, that’s why I think that article is just a fluid mechanics model that makes assumptions hard to be confirmed.

For adiabatic conditions, the calculation for this model can be performed by hand. Some guidance you can found in the article "Gas-Flow calculations: Don’t Choke". I’ve downloaded the article from AFT site. Mr. Trey Walters is the President of AFT (Applied Flow Technology).

Anyway, the real case of PSV is a much more complicated simulation, so I would prefer to have the results from AFT package- Arrow is the module for Gas-Flow calculations.

I don’t know if what I've written clarifies your doubts. Probably neither of your formulas is what you need.
In my understanding it's important to simulate what is happening through the piping system rather to know what is happening in final shock wave.