Chrysler's shared the 722.6's and 722.9' transmissions during the illfated Daimler/Chrysler era.
The W126 500SEL had an old 722.3. Some Porsches shared that transmission.

I see from your sig that you have 265,000 miles up on your 500SEL. That's getting up to the amount of miles your tranny might need a rebuild. I.M.H.O. I suspect the front pump.

I would change the fluid first.

The valve bodies in these transmissions do get some sludge in them over time. When they gunk up to the point of faulty operation that generally means that wear in the clutches etc has got to the point requiring replacement/rebuild.

Later version transmissions would delay the shifts when first starting out from cold to warm the fluid up quickly.