What Mileage is on the Odometer?
The approximate number of seconds before it goes into First Gear?
Some hesitation going from park to drive is relatively normal on an old Transmission. Could it be a B2 Piston Seal issue of B2 Piston issue will not be known until the Piston Fails.
The B2 Piston and related parts are accessed from the outside of the Transmission.
There is no sort of adjustment you can fool with when you change the Filter.
There is Spring Kits to try to correct some shift issues but I believe that is after the Pressures have been checked and re-adjusted to see if that corrects the issue.
The condition of your Transmission sounds better than mine.
On mine it is the reverse that has the delay and slightly harsh shift. On the older Transmissions there was an External Band Adjustment that could help that some. I have not read of any way to adjust the Reverse Band on the 722.315 Transmissions. If there is a way maybe someone will chime in.
I have not ever checked the Pump Working Pressure or the Modulated Pressure on My Transmission.
The Flaring can be a Vacuum issue and what position the Accelerator Pedal is in changes the Vacuum going to the Transmission Modulator.
Transmission Vacuum and adjustments
Mercedes-Benz Transmission, Steve Brotherton, ImportCar, February 2002
When I first became a Member of the Forum I read to use Lucas Transmission Sealer Conditioner. But, that recommendation seems to have faded in popularity.
In My case it helped and also reduced the leakage from the seals. It is unknow if it will help in your case.
To me the Lucas Stuff reminded me of STP but pink. So I am thinking that just like STP increases the viscoisty in Engine Oil I believe it increases the viscosity of the Transmission Fluid. Thicker Fluid would raise the pressures and at the same time decrease leakage. I don't know if that is what it really does.