Welcome to this "Star-Crazy" Forum!
I'm not a pro either, but have the following thoughts.
Search for the "Floating 300E" threads. Also look for threads regarding "thrust arms" in the rear links and "rear subframe mounts."
You might ask if your alignment was a 4-wheel alignment. If only the front end was done, you're only 1/4 finished with the job, I believe.
My 300E was terrible for awhile. It's much better now - I had all of the rear links replaced (probably unnecessary, but certainly the thrust arms needed replacing), the steering damper, front and rear shocks replaced and the rear subframe mounts and differential mounts replaced. I used Bilstein HDs, by the way. I love them - they're not too harsh for me; I get asked about it all the time. Count me as weird, but I find a stiffer ride more comfortable (probably psychological given the way I drive). I had a four-wheel alignment done as well. It's still not perfect, but I may be too picky, or I may be erroneously attributing some of my car's minor neurotic behavior to the suspension rather than (i) the pilot, or (ii) the tires, which are Pirellis. The Michelin MXV+4s which preceded the Pirellis, however, acted exactly the same.
I have been told by 2 competing techs and have read often on this forum that 300E handling pieces start to go south at around 100K. Believe it to be true, especially the rear thrust arms. The replacment parts for these are redesigned (actually, they are taken from a heavier class) and I believe the kit contains a different bolt as well.
A short while ago, when I had a little extra fun money (not now) I asked JCE about his Sportline suspension and he referred me to the link under "CARS" at the top of this page. When all was said and done on the work I referred to above (including the work I did myself), the cost would've been about the same to bolt in the Sportline stuff, although the Sportline package doesn't include the subframe mounts and rear diff mounts (or does it?).
Think about that!
2003 Dodge Durango SLT
2002 BMW E39 530i Sport
1988 Mercedes 300TE
2003 Chevrolet Suburban