Comparing a parkerized steel barrel to a parkerized aluminum frame is apples to unicorn fluff.
odugrad, stop using CLP. It's not a good corrosion preventative. To stop the rust from returning, you must kill it at the source. If your barrel is parked, something has gotten in the pores and to the base steel. If it's water, you need something to get down in there and displace the moisture.
Parkerizing is porous. It works by absorbing and holding oil which needs to be reapplied as it will evaporate over time. What I'd try is using a good water displacer. The two that come to my mind is Corrosion X and ACF50. Corrosion X is smelly, sticky and nasty and ACF50 may not be easy to find. I believe Mouse Milk may work but I'm unsure of it's water displacing abilities. WD40 is supposed to displace water, but in reality, it's not a good choice for much of anything. It tends to leave behind a gummy residue that does nothing for your weapons.
The simplest thing to try is to soak the affected areas in synthetic gasoline motor oil of the thinnest viscosity you can find. Make sure you re-oil the entire barrel to give the parkerizing a chance to absorb it