For what you are trying to pull off, you need a carbine length DCM type float tube.

The tube will be the barrel nut and tighten to the end of the upper receiver to make the under float tube rock solid, then  hand guards will clip to the tube to make them solid on the tube.

https://www.ar15.com/forums/ar-15/Free_float_DCM_style_CARBINE_length_tube_/4-275413/

In your case, nothing is holding the end of the front hand guard clip solid, and the problem at hand.

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Or, if you don't need the front hand guard to float on the barrel, need to drill and tap the front hand guard ring and back of gas block, to secure them together instead with bolts.  Right now, the front guard clip is just floating around the barrel with a lot of gap to barrel, and this gap movement if causing the wobble problems.  Granted that you have he gas tube on the top, but should be fine to attach the front ring to both sides of the back of gas block.





P.s. if the front gas block was steel, the could weld the ring to back of gas block, like you DCM a M14.

Here is the screw method on the M14,


While prefer to just do a full tig weld the ring to gas block on the other side isntead.