I started to give advise on the ABS system, but after re-reading your initial clues, I think it may well be a bad PS pump. The pulsing is fast ith ABS system activated, its like a Brrrrrt!. maybe 20 pps, you say you feel only a few pps (pulses per sec). You do NOT feel anything in the brake pedal when it pulses, right?
If so that sounds like the pump to me, based on when you accelerate slightly it goes away.
FWIW, the wagon uses a special pump also, as it has a separate SLS pump incorporated in it. Finding one is not going to be easy and the dealer will want a carload of cash for a new one but put a want out on the parts section and I'll bet a member comes up with something.
This is a strange thing I've never encountered before though. I have a bad SLS servo on my wife's '87 300D and it is not sensitive to acceleration, it likes to pulse just as the car slows to a stop while braking (brrrrt! sound and you feel the pulsing in the brake pedal. Never does it with no brakes applied.
DDH
PS yes there is a filter at the bottom of the PS fluid reservoir, worth changing along with the correct fluid. Probably hasn' been changed in years unless PO was really up on their maintenance.

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'95 E320 Wagon my favorite road car. '99 E300D wolf in sheeps body, '87 300D Sportline suspension, '79 300TD w/ 617.952 engine at 367,750 and counting!