NOTE: I'm not particularly happy with this answer. Notably because I've not used the equations myself and don't know if I'm representing them fairly. If another answer can improve on this, I'd be utterly delighted.
I believe you have misunderstood the relationships proposed in the book you link to. Here's a quote from the book I'll reference:
In general, the concept may be summarized as follows: We consider each planet separately, staarting with the largest (Jupiter). Each planet, together with the Sun, is considdered as a member of a two-body system, having a certain mass ratio $\mu$ (mass of the smaller divided by the sum of the masses of the two), a certain orbital eccentricity $e$, and a certain mean distance $\bar{D}$ (semimajor axis of its orbital ellipse). First, consider the pair Jupiter-Sun. In its orbit around the Sun, Jupiter creates a broad annular band about 250 million miles wide centered roughly on its orbit; within this band, no small third body can exist in a stable orbit, and one would not expect to find a major planet growing by accretion within this band. The dimensions of this "forbidden" region are functions of $\mu$, $e$, and $\bar{D}$.
Next, consider the the Saturn-Sun pair. The forbidden region created by Saturn is an an annular ring about 350 million miles wide wich does not overlap the forbidden region produced by Jupiter. It is as though each planet produces a standoff distance that is a function of its mass and its distance from the Sun, and within which other planets cannot orbit in a stable manner. This holds true for Neptune, Uranus, the Earth, Venus, Mars, and Mercury, as well as for Jupiter and Saturn. None of the forbidden regions of these planets overlaps any other. The only exception is Pluto. Ahtough Pluto's mean distance lies ourside Neptune's forbidden region, Pluto's orbit crosses into it; this may foreshadow an eventual catastrophic perturbation of Pluto's orbit by Neptune sometime in the distant future.
There are also wide gaps between certain adjacent forbidden regions within which small bodies can exist in stable orbits, notably the asteroid belt betwen Jupiter and Mars. Interestingly wide gaps are also present between the forbidden regions of Uranus and Saturn and between those of Neptune and Uranus, where small orbiting orjects (as yet undiscovered) may well exist in large numbers.
This provides a pretty good procedure that can be applied to any solar system.
Begin with the largest planet in the solar system. Repeat for each planet largest mass to smallest.
For each planet in turn, calculate the mass ratio.
$$\mu = \frac{planetary\ mass}{planetary\ mass + solar\ mass}$$
Determine (perhaps arbitrarily) the eccentricity $\mu$ of the planet's orbit. It might be worth assuming $\mu=0$ (circular orbit) until you work out the repeatability of this procedure.
Set the mean distance (semimajor axis) $\bar{D}$ for the target planet based on the forbidden zone calculations of all previous planets.
Calculate the forbidden zone. Curiously, I don't find the equations for that in the book you linked to, nor have I found them with an admittedly trivial Google search. I did find this article that lists equations that may be useful (they're for calculating the forbidden zones for moons), but reading that article, they're non-trivial equations. Are we straining at a gnat?1
NOTE: As I said, the equations in the article I reference are for moons. Honestly, that might be a more than adequate simplification for worldbuilding purposes. However, even those aren't equations aren't trivially processed. The equation below can't be blindly used (note that double-prime mark). I'm growing fond of the idea of forbidden zones as I learn more about them, leading to me wondering if a simplified equation can be derived that could allow non-PhD worldbuilders to crank out adequate solar system designs.
$$R_{2,3}''+(1+\xi)* \left( \frac{\lambda m_1}{|R_{1,2}|^3} \right) *R_{2,3} = 0$$
where...
$$\xi= \left( \frac{(m_2+m_3)}{m_1} * \frac{|R_{1,2}|^3}{|R_{2,3}|^3} \right)$$
and...
- m1 = mass of star
- m2 = mass of planet
- m3 = mass of moon
- $R_{n,m} = \bar{D}$ = radius vector between two bodies
Note: I mentioned I wasn't particulary happy with this, right? If you assume $m_1$ is the mass of the galaxy's black hole and $R_{1,2}$ is the distance between that black hole and the sun, then you should be able to use the equation by treating the planets as moons. However, despite the article's enthusiastic conclusion that this produces results for forbidden zones, I don't see how that can happen, suggesting that the article is written for people trained in the art and not mere mortals like me. Ugh.
Place the planet in relation to the other planets in the system. This will be an interative process because forbidden zones should not overlap (Pluto's exception should be treated as that). You may discover that, for example, your second planet calculated an overlapping forbidden zone because your initial assumption about $\bar{D}$ was too close to another planet, forcing you to change $\bar{D}$ and recalculate.
It's natural for gaps to appear between planets.
Rinse, wash, repeat....
Most of the planetary data you provide isn't relevant to this issue. A planet's radius, for example, isn't considered for calculation of forbidden zones. Neither is the planet's density. Just its mass.
1 Let me clarify my statement. Back when I was a teenager I spent several weeks reading a book about the mathematics of rocketry and working through the equations to design a rocket. It was a TON of work, but I remember my parents and teachers being proud that I'd worked it out. Beaming with juvenile pride, I built the rocket I'd designed. It didn't work. Not even close. In fact it was a disaster. What I learned is that there's a HUGE difference between aquiring and learning how to use a hammer (tools) and actually knowing how to build a house (celestial mechanics). Please accept this wisdom for what it's worth: there's a reason why people spend years in education. If your audience can't appreciate when you're right and can't know when you're wrong, there's little value in getting every possible detail right. Thus, straining at a gnat.
