Oh, I was waiting for you to fill out the second part of the challenge, the impacts on the other parts of the rules. You said you needed some time.
Too bad, I was waiting too :-[
So, how would this influence the Habitability Modifier and Life Zone Inner/Outer Radii of the Primary Stats Table? Further, how would this influence Step 3: Filling Orbital Slots?
I'm sorry for the size of the following text but you asked for it... O:-)
An extremely brief overview of planet formation: Terrestrials and giants initially start out pretty similar, as a large piece of rock. Only at a later stage, they begin to differ. At first, the inner planets are (on average) slightly larger because the shorter orbital periods increase planetesimal collision rates but are subsequently unable to gather much gas because the star has already blown away the disk from their orbits, hence, they become terrestrials. On the other hand, the outer orbits are still surrounded by gas which is accumulated by the planets.
So, at some point, the inner planets only grow by collisions with other planetesimals which is a statistical issue, depending on a random initial distribution of disk mass and angular momentum. Thus, their final size / mass can vary statistically. In contrast, the mass of giants is dominated by the accumulated gas which depends on the density of the disk. Since this density decreases with distance to the host star, the outer giants will not gather as much material as the inner ones and cool faster, resulting in the temperature and chemical composition known from ice giants. In the outermost parts of the system the planet formation is extremely slow because the long orbital periods reduce the collision rates between planetesimals to almost zero. For example in our system, the gas disk is gone for 5 billion years now but there are still planetesimals (Pluto etc.) around that have not formed a real planet yet (and will not before the Sun goes boom).
Asteroid belts are another issue. They do not appear at random but are found in unambiguous locations. There are 3 possibilities. One option is extremely far outside of the system where planet formation proceeds so slow that not even planetesimals have formed yet. Another are early planet formation artifacts collected near Lagrange points of planets. The last variant corresponds to our asteroid belt between Mars and Jupiter. The gravitational perturbation from a nearby protoplanet/planet inhibits the formation of any larger bodies there because the orbits are not long-term stable. Such asteroids belts would be scattered out of the system rather quickly but ... (blah blah something about orbital resonance that you don't want to hear). Therefore asteroid belts are found either at the system's rim or in the proximity of a large planet (but outside of its Hill sphere).
In the first billion years, a large number asteroids/comets (mostly made of water ice) from the outer system enter the inner system (due to high eccentricity orbits and scattering) and collide with the planets. Only this way, the inner planets can form a denser atmosphere and eventually oceans.
In the light of this... There is a strict hierarchy with the terrestrials at the inner orbits, gas giants at intermediate orbits and ice giants at the outer orbits. Of course, gravitational scattering could theoretically change this order, however, typically planets are either kicked out of the system or fall into the star. Therefore, a terrestrial planet will hardly be found on an orbit outside of a giant planet. The reason is that the giant would first have to destabilize the orbit of the terrestrial and then, just when the smaller planet is almost ejected from the system, stabilize its orbit again. Winning a lottery is an everyday event compared to these odds.
Because of this I'd recommend to get rid of random assignment of the object types. As replacement one could go for rolling the numbers of terrestrials, gas giants and ice giants which would have to be assigned in the typical order.
Another aspect would be the dependence of planet types on the stellar type. More massive stars form faster and yield a higher luminosity. Therefore, planets would need to form much faster as well. Although it could indeed be faster because of the higher density of protoplanetary disk, the Hill spheres (sphere in which a planet dominates the gravity field) of the protoplanets is also much smaller. This means, that overall mass that can be accumulated before the disk is blown away is most likely smaller. More massive stars are also less likely to have a companion star...
Another problem is the planet formation at larger orbits. Orbital periods are proportional to 1/sqrt(stellar mass) while the stellar luminosity is proportional to (stellar mass)^4. This means that it gets harder and harder to form planets at larger orbits for increasing stellar mass. In this reference, your orbital assignment in Step 2 does quite the opposite (for obvious playability reasons).
The conclusion is that stable planetary orbits will be packed much closer around more massive stars. In addition, more massive stars will have planets in much smaller orbits and are less likely to have Jovian planets. Because the habitable zone drifts outwards and the planet formation zone drifts inwards this also means that habitable planets are less likely to exist. Water transport into the inner system could become a problem because the ice line lies far out and the hot star might evaporate the comets before they can hit the planets. Hence, I would not expect water-rich world.
Vice versa, lower mass stars will likely tend to form planets at larger orbits. The smaller density of the respective protoplanetary disk will slow down planet formation but on the other hand, the star formation takes ages and the disk is not blown away as fast. This could speak for higher numbers of gas giants compared to terrestrials but it is also possible that one end up with hundreds of smaller protoplanets. Also there is a good chance that the habitable zone lies so close to the star that only planetary migration could allow a habitable world but this would require a re-stabilization of the orbit (and seriously why should the mechanism that spirals the planet towards the star suddenly end in a convenient moment). Water transport to the inner planets is probably not a big issue because the ice line is very close to the cool star and the radiation field is weak. Therefore, the likeliness of water-rich worlds is significantly increased.
This brings us to UV, X-rays and Gamma rays. I noticed that you mention their influence on habitability on several occasions. The UV problem for the K stars was a good catch. But there is another interesting influence for the M-dwarfs. These objects show hardly any UV radiation except for strong Lyman-Alpha emission on levels of the Sun. This is interesting because it splits up water (also in form of ice) and releases O_2 and O_3 to the atmosphere (keyword bio-marker). (By the way, there's a typo on p.3 under Life Zone Maximum: replace CO^2 with CO_2). Although oxygen does not yet make a habitable planet, liquid water does neither. But both are good indicators for habitability and, therefore, an ozone layer and sufficient oxygen in the atmosphere can be considered as an extension of the habitable zone beyond the typically assumed orbits.
Of course, the problem is extremely complicated. Realistically, the habitability modifiers that you listed seem too good to be true. I'd expect much more harsh modifiers for non-solar star but that would definitely kill all the fun as well as collide with BT canon.
Anyway, some of the abovementioned stuff could help to set up a more reality-oriented creation mechanism.
Alright, challenge concluded? Or do you have further questions I can help with?