If the Sun was born in a tight group with many other stars, those "golf balls" would be a lot closer together in your analogy.
And, I suspect that a protoplanetary disk tends to get flatter as it evolves into planets. Matter in the disk probably oscillates across the thickness of the disk , attracted back toward the central plane by gravity of the disk material, itself. That is the way stars behave in the galactic disk. As the planetary disk matter gets swept into planets, I would expect the disk to get thinner and the planets more aligned into a flat orbital plane.
So, if something tilted the orbit of a large planet relative to the evolving disk, such as a rogue planet escaping another star forming nearby, I think that could result in the large planet then imparting a tilt to the rest of the disk as it evolves and flattens.
Just a hunch, because I do not run simulations, myself.
But 7 degrees is not much. The Earth's magnetic field was tilted by more than that in 2001, but is now tilted by only about 3.6 degrees. See
https://en.wikipedia.org/wiki/North_magnetic_pole
With the Sun reversing its magnetic field every 11 years, it seems to me that its internal structure is not very rigid. Do we even know how its poles have moved over thousand of years?
A belated but long comment. It would indeed have been good if the article gave a general explainer as both of you make some good arguments but are somewhat confused about the process of planetary system formation.
The key point here is that protoplanetary disk formation is due to
non-gravitational effects. Gravity alone does nothing but keep objects on an orbit forever (well, apart from perturbations by other objects). However, in a collapsing cloud, objects cannot move freely for long: sooner or later, they will collide with other objects. There are collisions at the atomic level, which acts like friction; and once dust particles, meteoroids & asteroids form, there are macro-level collisions between solid (and liquid) bodies. There are also other non-gravitational effects (like magnetic fields, loss of moment via radiation) but collisions are the most important.
Now, which are the orbits on which collisions are the least likely? It's concentric near-circular orbits in the same plane. And that will be your end state if you start with a cloud of even a small asymmetry, because all the objects on elongated and inclined orbits are much more likely to collide.
For larger objects circling a star, gravity during close encounters also does play a significant role in changing orbits, but the overall effect runs opposite to collisions: the orbits become more diverse in inclination & eccentricity.
Disk formation is a case where order arises from random events. but, at the core, it's a random process, and never complete. Collisions (and close encounters) will be much less frequent in the less dense and slower-moving outer regions of the cloud, while close encounters between the much more numerous smaller objects and the much more massive larger objects tends to clear the inner regions and add even more objects on eccentric & higher inclined orbits to the outer regions, so these outer regions of the disc will be much less flat. There will be (much less frequent) collisions and close encounters even in the narrower parts of the disk even billions of years after the formation of the disc, and the collision debris will form new objects on eccentric and inclined orbits, but they won't stay there long, as they are likely to sooner or later suffer further collisions & close encounters.
For the purpose of what you have discussed, one possibility is that the difference between the Sun's axis and the axis of the Ecliptic it's just down to the randomness of the formation of the Solar System.
The instability of the magnetic pole of an object says very little about the instability of its rotational axis. The latter is based on the rotational motion of a lot more mass and there is the issue of the conservation of angular momentum. An object passing close to another will do almost nothing to its rotational axis. The most another object can do through gravity is create internal friction through tidal forces through a longer time when the two objects circle each other, which can slow down the rotation (while angular momentum is conserved by transfer from the rotating motion to the orbital motion), but this is a process on a timescale of millions to billions of years. This and similar processes can also change the rotational axis of a planet on longer timescales, but is unlikely to have affected the Sun (a much more massive object with a lot more angular momentum) a lot.
For the Sun's axis to change relative to that of the protoplanetary disk, a collision with another larger body would be a better possibility. However, this would have to occur very very early in the formation of the protoplanetary disk, because the orbits of the planets would be all over the place if a large intruder had passed through. The same applies to the possibility that the protoplanetary disc was perturbed by another star passing through and coalesced along a different plane. But, as you say, this would be much more likely with infant stars being placed much closer to each other when they form than they are in the Sun's vicinity now.
academic.oup.com
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