Nuclear thermal rocket shadow shield calculation?

Please have mercy on me and offer some help.
I though it would be simple, but I quickly got in over my head.

The problem: given a nuclear thermal rocket engine with
a power level of M megawatts, an acceptable crew
radiation dosage in Sieverts or rads, and a distance
between the crew and the reactor

Calculate: the thickness and mass of the required shadow shield.

SPACE PROPULSION ANALYSIS AND DESIGN by Humble, Henry and
Larson says a "typical" shadow shield is, starting at
the reactor: 18 cm of beryllium (neutron reflector),
2 cm of tungsten (gamma shield with some neutron shielding)
and finally 5 cm of lithium hydroxide (neutron absorber).
This attenuates the gamma flux to 0.00105 and the
neutron flux to 4.0E9, and has a mass of 3,500 kg/m^2
in shadow shield area.

If this attenuation is insufficient, additional
centimeters of lithium hydroxide or tungsten can be added.
SPAD had a table:

NEUTRON REDUCTION (ADDITIONAL LITHIUM HYDROXIDE)
X0.5 (+0.205 cm)
x0.2 (+0.477 cm)
x0.1 (+0.685 cm)
X0.01 (+1.365 cm)
x0.001 (+2.048 cm)

GAMMA REDUCTION (ADDITIONAL TUNGSTEN)
X0.5 (+0.564 cm)
x0.2 (+1.308 cm)
x0.1 (+1.872 cm)
X0.01 (+3.744 cm)
x0.001 (+5.616 cm)

So if I am understanding the table, if
gamma attenuation factor of 0.00105 is not enough
and you need 0.000525 instead, you'd need a gamma reduction
of x0.5. The table says this requires an additional 0.564 cm
of tungsten for a grand total of 2.564 cm of tungsten.

Since tungsten has a density of 19,300 kg/m^3, does this
mean that an additional 0.564 cm of tungsten would increase
the shadow shield mass by 109 kg/m^2 ?

Where I ran into trouble is trying to figure if a given
attenuation factor is sufficient. This depend upon
the intensity of the radiation flux from the reactor.

SPAD said that 1 rad = 2E9 MeVs / cm^2
and each fission event produces approximately 14 MeVs of gamma
rays and a bit less than 1 Mev of escaped neutrons.
It also said that one fission event produces
3.206E-11 joules.

Here's where I become (even more) confused.
The question is given the megawattage of the reactor,
how does one calculate how many rads or grays of
gamma and neutrons it is emitting?
(these fluxes can be multiplied by the attenuation
factors to yield the chronic doses produced)

To my unsophisticated eyes, it appears that if I
convert the megawatt rating of the reactor into
joule-seconds and divide by 3.206E-11 I'll have
the number of fission events per second.

Multiplying the number of fission events by 14 will
yield the Mevs of gamma rays and multiplying by 1
will yield the Mevs of neutrons.

And dividing by 2E9 will give rads.

This can be reduce by the inverse-square law
due to the distance between the crew and the reactor.

Multiplying both the the quality factors will
give rems. This can then be compared to
maximum allowed yearly dosage charts.

Now is the time to laugh hysterically at my
hopeless naivety and point out the flaws
in my reasoning.
.

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