In order to both polish the barrels to “chrome” and then subsequently get the slow rust solution to gently bite into the polished steel, you need to develop a method that allows that to happen. That’s a trick I’m not quite ready to part with quite yet.
I have not had good luck getting Mark Lee solution to bite into highly polished steel. It doesn’t work very well for me on anything polished to 320 or higher.
Ensure you’re also using a saturated solution of baking soda and water to neutralize and let them sit in that for at least an hour or two. That was a great and very helpful tip from an old time barrel blacker that I got a while back. It makes a difference.
I have a couple of tricks also. The shine is possible, and honestly not all that difficult. I'm not sharing either.

I never polish beyond 400gr and usually only 320. Experimenting with finer grits never showed any improvement to my eye.
The baking soda neutralizing is new to me. Never done it. Honestly not even sure I have heard of it before this thread.