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Sounds like you know more about suspension than your modesty allows.
I imagine you have already adjusted the tyre pressures? If not I would start there with something like 32 front 36 rear, which works well on my M900Sie but might need a pound or so more on the heavier S4?
Next I would look at the tyres themselves starting with the date stamps. I would change anything more than 5 years old as a matter of course, or even getting near that if they feel hard and stiff or show any sign of degradation/cracks.
Also look at the wear pattern, as they may well have prematurely flatted if they were run with too much pressure? Even a virtually invisible flat on the rear will induce horrible handling characteristics, which usually gets blamed on the front.
If the rear has a flat then the front will most likely have corresponding "pyramidal" wear which can also be hard to spot, but will play up the handling, particularly at that roll in point, but usually be okay when cranked right over, which you seem to allude to?
Next, and in short order I would change the fork oil, as you obviously intend to do. It might explain the apparent lack of rebound damping as you accelerate? Low oil might facilitate some compression damping as the forks go down into the oil, but they could be coming out of the oil on the way up and so loose rebound damping?... Possibly?
Even good suspension will struggle against the above faults, so it's always best to check the background (cheaper) things first and go from there.
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