Constrained Rifle to Right hand - Floats in left hand issue - Only for cinematics/animation

I’ve an issue I’ve spent some time looking into, but not been able to solve (aside from just manual keyframing).

I’m using the ‘Constraints’ feature (in animaiton panel) to constrain a rifle to the right hand of a soldier. This works fine, but it can at times float in the left hand. I know there are ways to fix this using the Animation BP (e.g. shown here: UE4 Tutorial: The Right Way to Do Left-Hand Weapon IK – Zag's Blog)

But I’m not using an AnimBP and just animation seqs in a level sequence to create some cinematics. Any suggestions of how to fix would be great - thanks!