1989 300TE transmission with 'slow' reverse

The reverse gear takes at least 20 seconds to engage, much worse if the transmission is cold. Once engaged, there is no slip. All forward
gears are working with no issue. The ATF level is good and it looks clean/red.
Based on search in past postings and lookin at the parts catalog, my understanding is there is a clutch pack controlling the reverse, but I don't see a piston. Is there one, like the B1 and B2? And how is the clutch pack engaged? Is this someting inside the valve body? A seal?
I am going to replace the ATF and filter. If the problem is deiniftely in the valve body, is replacing it possible from under car without dropping the transmission? Is it (replacing, not rebuilding) a DIY job or I better leave to MB transmission specialist? I have done most maintenance on my MBs by myself so I don't mind replacing (or learning to replace) it by myself too, if it is possible.
The car is W124, 89 300TE. Transmission is 722.358 (4 speed automatic). Mileage is about 177k. I do not know its past history.
Thanks in advance.
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