The only carry handle sights I have used that are worth a damn are Colt and custom aftermarket.

You should be able to kick up a custom sight with a stop that prevents that motion with an internet search.  Look amongst stuff for NRA High Power or "Across the Course" shooting.

Here are the first four places to check -

Creedmor Sports
Champions Choice
Champion Shooters Supply, and
Sinclair International

I have not hunted one down for a long time.  The other choice is to machine a modification.  A good place to look for help is one of the High Power forums and the CMP forum.  The cost will be high, but you will also get a much better sight.

From the above photo, you can see that the sight housing is only single sided detent'd to the receiver, so the twisting is in fact normal and desired.  Hence if the rear sight takes a impact, it going to return to the original position since it has some give, and in fact with the housing only riding the one side, it helps is retain its zero as you can cracking back and forth for the elevation changes.


As for NM rigs where you going to make sure that the rear sight does not take a impact, and that you need  the housing true to the receiver line due to  a hooded aperture (and even with a lens piece), then there are mods to guide rod the housing to the receiver instead.


Here, since you are going to change out the 1/4" moa to a 1/8" MOA movement rear sight that does not use the two piece split design dial, you will use the Allen wrench channel in the sight for the  front guild rod channel, drill for a rear channel and them install the guide rods into the receiver at that locations

The cock of the sight housing in the upper receiver is normal.  


Not normal is when the front edges of the housing itself, is past the wider lips of the receiver sight tracking pads isntead.


So although your sight housing is slightly more cocked than say a brand new receiver, the amount of cock to the housing tracking the pad is normal.
Hence over time, the large threaded section of the sight housing will wear the receiver channel for it in the receiver from rasing and lowering the sight, and this allows the rear sight to cock back more/ leaves a slightly wider gap between the front of the housing to the back of the receiver wall, and causes the slightly more gap.


The receiver channel for the housing threads you don't really want to screw with, but if the cocking of the housing is really bother you and you don't want to have to NM the sight to get it not cocked at all, then you can just pull the rear sight housing and build up the receiver  right back tracking pad wall that the housing is going to track with Black pigmented epoxy isntead.