If your vet rules out health problems as causing the behavior, then the next place to look is very closely at his environment.
If something in his environment has changed (the litter box liner, as only one small example) then he may simply be demonstrating his dislike and mistrust of the offending change.
But, if as you say, taking away the liner hasn't changed the behavior, then look deeper. Have you brought any new furniture into the house, rugs, or other decorative items? How about cleaning products? Are you cleaning with something different than you have used in the past? Are there any cats outside your home that he might be aware of? If so, then he very well could be displaying extremely normal and instinctual marking and territorial behaviors by leaving his ... business ... where he thinks other cats (real or imagined) will know this is his turf. Are there new people coming into your home? How do they interact with this cat? Could it be that there is someone mistreating him without your knowledge?
Please let us know what the vet says,