Rifle correctly cleaned with CLP, including scrubbing the chamber with a chamber brush, the old fouled CLP patch/wiped away, then a fresh coat of CLP on the upper receiver bearing areas.
As for the later part, the easy way to do this, wet the B/C inside and out with a coat of CLP, install the B/C into the upper, lock the upper home, then empty cycle the rifle a few times.
Also, since the rifle is being cleaned and lubed with CLP, do not use other lubes or solvents like hoppes, since it not going to mix well, and make a sticky mess.
At most, if you want to first start off with cleaning the bore before you scrub the chamber, then something like Sweet solvent does not leave behind a residue, not does it take a lot or scrubbing to remove copper fouling with it out of the bore. Just rememeber to run dry patches after you use Sweets to get the last of it out of the bore, then you can switch over to chamber scrub mode with CLP and the chamber brush next.
If correctly cleaning and lubing the rifle do not solve the problem, then get ATI on the phone to resolve the problem isntead (why you buy a factory build gun in the first place).