Hi Cake,
yes the price of the xtr groupset components are up in the gods, so to speak! I've had a look at the model you have got 'on line' but can't see them close enough to what what magic can be worked.
I have some the xt group set on my mountain bike, and Xtr group set on the Thorn expr, And have to say they are good. The xt however can't be adjusted like I thought but the xtr definetly can. both models especially the xtr give absoloutly no side play at all.
As you said, the best thing to do is try to see what comes apart and where the excessive movement is coming from, but be carfull not to over shim as when you put the binder bolt back in the arms may be to stiff to move or return to nuetral again, perhaps a close up picture of the area may shed a little more light on the possabilities.
Email if reqd.