When people normally talk about "natural overdrive" they are usually talking about driving the preamp of the amp into break up, from what i remember the MG series from Marshall are solid state so its not going to break up like it would with tubes.
GOTTA GO WITH TUBES BROTHA!!
I'm not sure how to program those new marshall mg's so cant help you there, sorry
But as far as driving tubes i crank up the gain on my clean channel to around 8/9 and the volume to around 5 (the loudest i can crank it and hear an audible difference in volume). But then when the volume is cranked you open another door and key to tone, Driving Your Speaker(s).
One thing i had a problem with tube amps is when i front-ended my boost pedal i'd reach the highest amount of headroom available on the amp and it would break up which i wouldnt want, i just wanted it to be louder, not more distortion
i know your trying to get away from pedals, but one thing i have done recently is
Put a boost pedal in your effects loop. this puts the volume boost inbetween your preamp & power tubes so the preamp isn't getting pushed anymore, its just increasing volume which was what i was going for.
***I'm not sure if the MG has an effects loop but you can try having one clean channel you use and one overdrive channel with a boost in the effects loop for your volume jump i think your looking for!
Hope this helped you!