Interfering with play?

[RefereeX]

Great insights from everyone. Thanks. Now that we have the benefit of the video and hindsight, would the correct call be to award the goal because ref played advantage on the push in the back that put the player into an offside position?

If we determine that the player in an offside position has comitted an offside offence (i.e. made an obvious action that impacted a defender) then there is no way to play advantage from the push. One offence can't counter act the other, as the offside offence has still occured, so the options would be offside, or penalty if you felt the push was strong enough.