The W124s are tight handling vehicles and should only wallow about only if the suspension is worn. The rear is especially prone to causing this condition, there are several links which the bushings wear out and if yours are worn then it may feel weird in a sidewind also a check for this condition is that on acceleration from a dead stop the car will want to drift sideways even without any wind. If your fighting the steering then maybe you need some new rear suspension parts, or the front as well.
The Sport shocks aren't any stiffer than the OE, but they are designed to run with shorter springs. Bilsteins are the way to go and while you are changing the struts you might want to consider the mounts, see if the rubber is getting cracked, they have been known to fail in some cases sending the front shock up to the hood
Also the nuts used on the shock towers are supposed to be lock bolts, I can't imagine one coming loose! I always replace them with new when replacing the strut mounts, maybe someone has reused them on your car?
You might want to look at gsxr's thread(s) on the suspension upgrades available, he has a table of the parts that can be interchanged on these cars. I am using heavier front and rear anti-sway bars which improved steering response a lot over OE.