TE
All I can relate to you is that I do swab after each shot most of the time, I can normally get about 4 shots off without running the swab if I needed to but after that it gets really tuff... I shoot T7 which I THINK burns a little cleaner than GOEX.
You did not say which MMP it was - It could be either the HPH-12 or the HPH-24 - I guess I am assuming it is a 24 the thinner of the two - there is two other thinner options... a MMP HPH-3p-EZ load and the Harvester 'crush rib'
I do swab the barrel - a windex patch -(not clean but to remove the bulk of the fouling) after each shot as that would be the condition of my barrel while hunting or even shooting at the range.
Hope you come up with some answers that will work for you.