IL76 cargo cabin is aprox ~18.5 m long, 3.2 m wide, 3.2 m high (725"x125"x125"), max width up to aprox 105" high, so your piece will fit.
If you want to pick it up ex USA or Europe, the only stage-4 IL76s are at Volga Dnepr and Silkway. They are not cheap if you compare to stage-2 IL76s but still much cheaper than AN124.
Volga is much more experienced with heavy weight and oversize pieces.
You don't really need hi-loader for IL76, but better talk to operator. They have onboard crane but I think you cannot use it for the box of that height.