You guys are answering your own questions instead of the OP's and saying things that are contradictory. The OP asked if polishing will remove his LSP (my answer is YES) and whether it will gunk up his pad (my answer is NO).
Does it matter if Z-5 is supposed to fill/hide light swirls (if you've actually used Z-5 you know it really doesn't do that)? No, it doesn't, because the OP has already said he's going to do correction.
You guys are making the argument that the reason he needs/wants to strip the LSP is so he can see the true condition of the paint so that he doesn't start with too aggressive a polish/compound--but if he's doesn't strip and doesn't see the full extent of the defects...how/why would he start with TOO aggressive a product...he would start with a not aggressive ENOUGH product. But since he is already seeing defects which are apparently too deep to be filled--by the time he removes them he will certainly have removed any shallower ones that might be masked by the LSP and revealed by stripping.
IMO the OP asked some specific questions which should be answered first, then you gentlemen can add in the "here's what I do" and why. Remember, the OP isn't a pro detailer trying to assess a customer vehicle, this is just a member trying to clean up his ride.