Some parts of the frame where the rust is just seeping out from those joints, I'd use that chemical rust cleaner and then clear coat finish it with spray can you get in automotive shops sections to seal it. Might be better this way rather than trying to match the paint which you won't match anyway, so its better to 'admit' the damage, because trying to hide it would look worse.
The bottom bracket mechanical cleaning with wire brushes on a drill and then apply that chemical that says on the bottle it reacts with the rust - it blackens it in the reaction, creating further rust protection that way and making it ready for paint (color and clear coat or just clear coat). Look for it in paint shops, but automotive I think carries it too.
And yes, dismantle it all, like that guy in the video. Doing half way job usually takes more time and gives half satisfactory end result, and you end up doing that in the end as you will be pushed to it anyway.
I just recalled, sometimes I was also using CLR to clean rust stains. Its worth trying that out since it can work wonders when it works. I always use it full strength and wear rubber gloves but it is pretty friendly, can wash it down in your sink. It is sold in gallon cans too if you might want to submerge the fork in it or part of the frame in some suitable container. In case of such volume use, I pour it back into another can to reuse it on other projects.
Last edited by vane171; 05-23-20 at 12:24 PM.