FF mirrorless only lightens the load slightly. Flange distance with FF lens is still a constant. The OP is saying they'd like a 1DX2 with gimbal use. Well, aren't you aware that steady-cams were originally invented for larger cinema film cameras? The 1DX2 is still considered a light B-roll cinema camera. A stabilizer like this can handle any HDSLR with wide/normal FL lens.
Glidecam HD4000 Stabilizer System