So the question of which we should use, which or that, in any situation is something that is prone to hyper-flexibility. Thank God! The restrictive/non-restrictive rule (I hear you, musick! ) is pretty clear, but there're still times when one or the other just sounds awkward even if it's the correct usage grammatically.
And sometimes, neither sound right. And I could never rememebr if there was a grammatical edict that would help simplify the decision. So, yeah, what Faldage says...if it sounds funny, the hell with it.

Which that or which is it proper to use
When a which or that is that which you'll chose?