bassman head is part of the equation
Some of the sound you are describing is the bassman head...it's not a high gain head and does NOT do modern distortion well (scooped mid, etc...). It's got the same type of sound as a twin reverb...when the amp itself distorts, the low end will get distorted and 'farty' and the high end will be glassy and cutting. Think 'surf' and blues style distortion.
To top it off some of the bassmans don't have 'mid' controls at all...
A Jaguar has some of the highest output single coil pickups around...plug one into a Marshall stack head and you will get more of the sound you want.
Do you have another head you could use to drive the 4x12? How about pedals? Try running an overdrive, fuzz, or distortion up front with EQ to get a fatter tone. Keep the bass control on the bassman down, and the eq on the pedals way up...
I have had a lot of success using a Boss Turbo Overdrive in conjunction with a Boss Hyper Fuzz in order to get a huge variety of distortion tones with
my Twin Reverb. I'm playing
a fender mustang, which has even lower output pickups than the Jag, but with the pedals overdriving the preamp stages in the amp, you can get a lot of different tones.