I do not think the different style of weights you have on the tires can adversely affect the handling. At high speed if tire balance was the source of your instability problem you would also note a pretty serious vibration.
I also wonder how the steering box can be causing your car to handle improperly at higher speed as you have not described a steering play issue at any speed. Typically play in the steering box is apparent at all speeds, and can be checked with the car in the driveway. Have someone turn the wheel while you watch the input shaft move and compare its motion with that of the steering arm on the output side. If there is a big "delay" while the input shaft turns to take up slop in the steering box before the output arm starts to move, then the box is loose. I have had good luck improving this condition on my older cars by flushing the power steering system and putting in a new filter, then tightening up the steering box with the adjustment nut on the top.
As was noted in the earlier posts in this thread, high speed instability is not a characteristic of Mercedes-Benz automobiles. In fact the opposite is true, it is one of the pleasures of driving one of these cars. So if you are experiencing a loss of high speed stability there is probably a suspension system problem. I would start looking at the shocks, as when they begin to degrade the tires and the suspension system are not held in the design location for the typical loads they encounter. The next thing would be bushings and other rubber parts as they degrade and loose the ability to constrain the motion of the wheels under loads. And out of balance tires can bring out the worst of all these by swinging the tire off the ground at high speeds. This is usually apparent though as the car will vibrate.
Replacing the steering box, especially at the price you were quoted, is not where I would start this quest. Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)