You've diagnosed it correctly. You're doing well with the soaks, but castor oil is a better oil to smother the mites because it's much thicker.
I fill a small container with the entire bottle of castor oil and dip the legs and feet in it, letting it soak in well under all the scales. Leave the oil on the legs and feet. It will slowly wear away. In a week, you will need to do it again to get any new mites that have hatched.
If your budget allows, there is a very good biological insecticide that works very well on leg mites and it only requires one soaking in it. It's called Elector PSP, completely safe to use on and around chickens.
It's a small 8 oz bottle of heavy concentrate that goes a long, long way. I mix a quarter teaspoon into a quart of water or double that for a deeper soaking. You do not need the oil treatment if you use the Elector. You can get it off Amazon, but prepare for sticker shock. I'm sold on the stuff despite the price. One bottle has lasted me years.
It can take up to a year for new scales to grow in. That's a very bad case of mites, and they are quite painful. He will be feeling much better in a few weeks.