Simulation of voltage sensitivity of ideal detector diode circuit
You seem to be plotting the direct voltage output, but that's not how they're describing it. What they defined is a voltage sensitivity, which they give as (\$f\$ in GHz):
$$\gamma_1=\frac{0.52}{I_S(1+\omega^2C_j^2R_SR_V)}\xrightarrow{C_j=0.1p, R_S=50,R_V=\frac{0.026}{I_S}}\frac{10^3}{f^2+2\cdot 10^6I_S}$$
Here there is a datasheet for HSPS8101 where, at page 2, they show both the SPICE parameters, and the equivalent schematic, in which the only variable element is \$R_V\$, as a function of \$I_S\$. Still, I used your values, and this is the result of (I also used your 0.9 GHz value for frequency):
.step dec param Is 10n 100u 5
.meas gamma1 param 1k/(0.9**2+2meg*Is)


which seems to be very close to the one in their figure 2 (the 1 GHz trace). If you want to plot \$\gamma_2\$ and \$\gamma_3\$, you'll have to use their formulas; no need for any schematic, by the looks of it, all seem to be usable as .meas directives.
BTW, I applaud your valiant efforts with the .model cards, but you can simplify that to only one:
.model d d Is={Is} N=1.06

and step Is as in the .step command above.

In order to avoid using the formulas from the paper and, instead, use the simulation, then you need to plot the sensitivity, which is given in V/W. Also, in the paper, at page 1, Voltage sensitivity, they say:

A detector diode may be treated as a current generator across the diode video resistance. The voltage sensitivity, \$\gamma\$, is the product of current sensitivity, \$\beta\$, and the video resistance, the inverse of the derivative of current with respect to voltage.

So the sensitivity of the diode could be extrapolated to the current setup as V/W = V/(V*I) = 1/I, or the reverse of the current through the diode. Using:
.meas Iavg avg I(D1)`

results in this plot:

The actual dynamic resistance would be very similar, (Vin-Vout)/Iavg, as given by:
.meas Vin avg V(in)
.meas Vout avg V(out)