I found this video, and decided to do like him. He puts some kind of extension on his power drill, and on the end he puts a tiny 1 inch steel wire wheel. He drives the wheel up and down in the seat tube for some time until the rust is gone.
I tried hard but never found a wirewheel this small in my country, at least not one that would fit on an extension. So I improvised.
I bought a piece of 12mm round timber. In the end I cut a 5cm slit, using a hacksaw to make the slit as thin as possible. I cut a 5cm wide strip of the most coarse emery paper I could find, inserted it into the slit and wound it around the pole.
The paper was sort of flapping, since when rolled compact together, the diameter was not as big as the inside of the tube. I thought this flapping was good enough, but after some time very little had happened. So I putting pieces of toilet paper in between the layers/windings of emery paper to increase the diameter. In the end I had a perfect diameter that I was able to fit into the tube, while it was still pressing on the sides.
It took a few minutes to remove all the rust.
The diameter of the pole was too great for my power drill, so I cut it thinner with a knife. But it was very difficult to cut in such a way that this thinner part was parrallel to the rest, and therefore the pole was hitting/hammering when rotating. It would have been much better to have bought a 10mm pole.
I don't know about the pros/cons of using steel wire, brass wire or emery paper. I suspect that emery paper maybe wears down the material and not just the rust, and moreso than brass and steel wire. So maybe using a brass or steel wire wheel is still a better solution, but I actually don't know.
The only right-sized wire wheel I ever found, which could also be mounted on an extension for the power drill, was this one: link. It's a 25mm brass wire wheel, for 1.6 GBP incl shipping. But it will take a month before I get it from China. I would then use it with an extension like this one (link).