When applying the rust solution apply it only to the exterior of the receiver and barrel. Do not apply the rust solution to the interior surfaces of the receiver, only blue what shows.
As for the barrel,I don't believe anything needs to be done. Apply rust solution to the exterior only. You can do the threads and the crown but don't get any down the bore. I don't bother with a hot box, damp box, etc. Seems to be enough humidity in the air, winter or summer in NC.
After boiling the barrel blow compressed air through it if available. Then run patches through until dry. As hot as the barrel is after coming out of the boiling water it will dry very quickly.
The barrel bore should be unaffected by repeated boiling and drying.
Vlad