There has to be something with your cleaning methods that's causing this...
1) What oil are you using to wipe the bore down after cleaning is done?
2) What are you using to clean the bore with? (IE jags, cloth, brass or synthetic brushes)
3) How much solution (water, soapy water, windex etc) do you use to clean the bore out with?
4) How thoroughly do you rinse and wipe the gun down after cleaning?
5) Does your cleaning solution run clean by the end of your cleaning process?
6) Are you patches clean by the end of the process?
7) Is everything bone dry before you oil the gun?
8) Just because there might be something to it - what powder?
Since you're saying it's a heavy coat of oil, that suggests to me you're either leaving enough residue behind that it's able to rust through the oil somehow (IE there's still fouling left in the barrel that has either escaped cleaning in the lands, or has been wiped and mixedaround by the cloths, patches and brushes if not sufficiently rinsed), or the oil itself isn't suitable as a surface protecting oil.
I'm almost wondering if there's crud hiding up against the edges of the grooves that's escaping cleaning. In this instance it might be worth using wipe-out or a lead focused cleaner to really get in there and remove any remaining fouling and leading that might be causing this.
Edit - I see you answered some of it already
I clean the rifle with hot soapy water (not boiling just as hot as I can get from the tap), then solvent then many many patches till they come out dry/ clean. Then I oil a couple patches and run it up and down the barrel as well as oiling the outside. I've been using browning ultra fine gun oil. I only use black powder (Goex brand) and have never ran pyrodex in it. I will try a different oil and see if it changes anything.