I just did a green mountain barrel with LMF. The humidity is very low and the temperature is in the 40s to 50s in my shop. It worked fine but took a full 24 hours between the five passes. The end result was a dark even plumb color.
I like to card with a bronze suede brush better than the .003" wheel.
I have been using industrial window cleaner concentrate, a squirt of Dawn, then about half iso-proply alcohol and water as my de-greaser and general shop cleaner lately. If you work the de-greaser with maroon scotchbrite you will get down to bare metal.
I'd be tempted to etch the obstinate barrel slightly with muriatic acid after de-greasing. I'd try a quick pass, only enough to see a slight reaction. I'd then rinse it off with a lot of water. I'd then heat the barrel just warm and apply the LMF as normal.
Muriatic acid will cause after rust. I'd neutralize it at the end with strong ammonia or balking soda. I apply used motor oil on a warmed barrel when I am happy with the color. IT will still rust after oiling, so watch it for a week or so.