What you just described would be the standard GC/customer relationship. The GC should be responsible for the work. It's great you have a good relationship and lots of trust.
Some things you can do to look at the tile if you really like it. One way that you and your GC can test the tile is to take several pieces and lay them down polished side together - like a sandwich but with nothing between the "bread". What you are looking for is to see if they lay completely flat together or if there is "warpage" in the tile. Test that by pushing down on each corner of the top tile (one at a time) and see if it rocks slightly. Warpage can cause lippage during installation. If would be unusual for a natural stone to have warpage. Also lay out 4-6 pieces of tile side by side with no gaps and make sure all of the tiles are the same thickness. If they are not, then that can cause lippage during installation. If you don't find any issues, then the tile is not at fault.
The issue is then the substrates or the installers. Most likely the substrate. The GC needs to inspect the walls and floors to identify any issues. If there are issues, then a discussion on what it takes to fix the substrates and what the cost would be. (I assume the GC would pay for the new tile and installation.) If the substrates are within reasonable tolerances, then the installation is the source of the problems. If so, the GC and installer should come up with a plan to install new tile for you at their cost.
Good luck. It's always disheartening to have issues, but most things can be worked out. What is a rolling shower??
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Flooring, glass etching
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