After I soak hardware over night (or two for some beat up trixon stuff I just got). I wipe them down twice with clean dry paper towel. (I don't worry about a bit of paper shred because this is just the start.) I did used to soak in mineral oil, but the Dawn is easier to work with and less toxic all around.
Once they are as dry as I can get them by hand--which helps clear off the first layer of grunge, I soak them in WD-40--sometimes overnight. I figure WD is about displacing water, so it makes sense to my little mind.
Then I use clean cotton rags and dry the pieces singly by hand. Then a fresh spray of WD40. For the threads I use my thumbnail to track the thread grooves. Up and down a few times, changing the cloth surface as needed. With balky gunk, I sometimes need to give it another shot of WD40. (I also have a pile of toothbrushes when necessary.)
This all works to get the threads clean and almost shiny.
I don't use steel wool, though commonly recommended. Too much potential damage.
Chrome polish. Hand buffed.
Then I lube whatever needs lubing, since WD40 isn't the best for that.
My method is pretty labour intensive, but I only bother soaking stuff like this that is already old and beat up. Having tried to speed up the process in the past, this slow routine has proven most reliable for me.
good luck!