What if we chose a dipole moment for 'Oumuamua consistent with a superconducting medium, just to be conservative? That'd take some physics in and of itself just to get a best guess and some error bars. Like I said though, it still might not matter, because if we're seeing a quasi-chaotic rotation, there's no preferred orientation over an 8-ish hour period. But I guess it's possible that for big events (like coronal mass ejections), the shock front arrival in the solar wind could do some pretty big pushing or pulling via magnetic coupling. I would wanna see the 'Oumuamua position/acceleration data, and then I would look at the solar wind data and make some cheap little analytical model of expected forces. I'd keep Oumuamua's rotation phase angle as a free parameter. The solar wind data source I usually use is FURLOUGHED, by the way :(.
Right, so, about the thing you actually prompted me about. The superimposed blue and red squiggles circumscribing the solar disk are the interplanetary magnetic field (IMF) orientation, which is very clearly a function of solar cycle. In the first panel, six years of data from Ulysses (a polar orbiting sun-observing satellite) is shown. The first six years were generally near solar minimum, unlike the second panel, whereas during the second 6 year orbit, the sun was generally near solar maximum. So if 'Oumuamua was ~20 degrees off of the solar equatorial plane (which is itself only +/-5 degrees from the ecliptic plane), it could maybe see a heavily-preferred magnetic field. People model this stuff hardcore, btw, and my bad if I've linked that before. But maybe big events could more clearly influence 'Oumuamua, either from a huge moment via comically large superconductivity, or a thin disk interacting with the solar wind ram pressure, or both. Again, depends on observational fidelity.
Edit: regarding the Ulysses data, I just read the written paragraph on the site and I didn't give much more than was already there, so specific questions are welcome.
As an example, if Mars were to have something hit it, and a chunk was to break off, it would be a magnetized chunk, albeit extremely weak compared to a superconducting moment (duh, srry, pedantry). The Martian mantle cooled below the Curie temperature like a billion years ago and the local orientation of the global magnetic field was frozen in. I dunno about asteroids, that study makes it sound like they can have pretty big magnetic moments. Comets are probably never magnetized whatsoever, or at least the one we've visited had no measurable moment. Maybe we should consider the possibility that it's neutral.
So just consider everything, good advice, am_Unition, thx!