Hi @leonardodaslade thank you for writing such a thoughtful article. @Kurzgesagt did a good job on their video too. But there's still a few things that I don't understand about the idea of moving the Sun.
Like, during the million years of travel, why wouldn't the planets end up trailing behind the Sun like the particles in a comet's tail (wouldn't their orbits deteriorate)? And then when the Sun arrives at its new destination and stops moving, wouldn't the planets crash into it? Maybe you could help me understand how gravity 'locks' the planets in place.
But also, if we could build a giant Dison Sphere around the Sun, then why not just build a smaller sphere around the Earth to protect us from asteroid showers?
If we could use electromagnetism to feed the Caplan thruster, then why not just use electromagnetism to redirect the solar winds? With the right 'shape' of electromagnetic field it may be possible to optimize acceleration by concentrating the solar winds. In fact, we might not even need a thruster, we could just drop the right combination and proportions of certain heavy elements into the Sun repeatedly to cause a propulsive reaction at just the right spot. Doing that could effectively turn the Sun into it's own thruster.
But like I said, I'd be worried about the planets losing their orbits during the million years of travel. (I think that every time the Sun's course and trajectory are altered, the planets and everything else effected by the Sun's gravity would experience an orbital reaction.)
We might even be able to create a small black hole and place it in a specific elliptical orbit around the Sun (much farther out than the planets, but just close enough to the solar system to pull a little bit on the Sun and planets every time it comes around the near-side of its orbit).
If humanity is technologically advanced enough when a problem arises such as a super nova or anything like that, then it may be more cost-effective (or simply human nature) for people to spread out among the stars, and maybe bring pieces of the Sun with us to keep burning like eternal flames.