So it turns out that you don’t need the table to clip through the ground. You can instead clip through the ground via a conveniently placed hopper (which you can see in action in the link below). It will only work when the bottom of it is facing the wall.
PS. If you take out the turret at the beginning fast enough (it only works with an SMG grenade or a rocket), Barney will immediately say “Great, I’ll open this up”. You can see that done with an SMG grenade with this link:
(Performed on Source Unpack)