Seems odd to me that both brakes work together in this drag effect. I believe the linkage is independent from the brake pedal back to the left/right axles, so to speak. But there is a brake valve where the right left brakes are activated, so maybe that is a place to look for this dual effect. One pic shows the brakes and the valve (dotted) and the other the valve. There is a brake valve kit with o-rings and such, so maybe there is some wear and tear that this valve needs. That I don't know.
Regards the 4wd being engaged or not while this happens....what you say?