If I look at an old Lyman Manual for the 7.7 Jap, and translate 45.7gr min load of IMR 4350...
Which old Lyman manual are you looking at to "translate"??
I've got the 45th Edition (1970) and for the 180gr jacketed, the starting load of IMR 4350 is listed at 47gr. for a velocity just over 2,200fps.
This is a light load (some 300fps below potential) and IMR 4350 is just a tad on the slow side for best performance in the 7.7mm Jap.
IMR 4895 is a better choice, and I think both 4064 and 4320 are both better than 4350 in that case.
The lighter the load, the less pressure to make the case swell tighter to the chamber. This allows more powder residue blowback to come back in the chamber.
The lighter the load, the lower the pressure, is true, but its not a matter of how "hard" the brass is pushed in total, its how much at which point in time and which point on the case.
The soot stains are are proof that the brass has not yet sealed to the chamber when the gas gets there, as the bullet moves out of the case, but, the case does seal to the chamber right after that, otherwise you would have gas blowing out the back of the action (and you don't, right??)
Slower powders burn slower and so build up pressure slower, and even though when full pressure is reached it will be as much or even more than other, faster powders, since it gets there slightly slower, it is more prone to APPEARING to be too low pressure and leaving sooty brass.
Upping the load level or going to a faster burning powder will probably reduce or eliminate your sooting problem.