My 1935 house has the same "problem." On every ceiling you can see the 16"x4' seams. It is also like that on all of the upstairs walls and many of the downstairs walls. We did a kitchen remodel a couple of years ago and it was interesting to see that the some of the walls were plaster and lath and some were either the gypsom or beaverboard described by others. I thought maybe they splurged for plaster and the living and dining rooms, but there didn't seem to be much method to the madness. I'm not sure whether its the plaster coat or the boards themselves but they are literally rock solid. I have to use a drill to hang anything, and many times the drill bits break. The grooves don't bother me as much as the peeling paint. In a few of the seams on the ceilings the paint literally falls right off. I'm not sure if I should blame it on a bad paint job or the materials in the ceilings. I also have the faux-tile that ken tn speaks of. It went all around the kitchen from the floor until about five feet up. It was in the bathroom and the half bath as well. In the kitchen the previous owner just plastered over it, but you can still see the pattern in places. I'm not sure if it was a stamp or something premade, but it is definitely not 4" ceramic tile. I don't know that the finish or paint colors have made much of a difference. It's very visible on the flat white ceilings and very visible on the various colors of satin walls. I did find many of the same old colors, lots of teal, green and coral around too.

UPDATE April 2018 - Went to a family owned hardware store and spoke with several of the employees. I explained my problem. and at their suggestion, bought a spring-loaded heavy duty shower rod and some Gorilla double sided waterproof tape. These inexpensive changes did the trick and I didn't have to drill into the tile. Problem solved.

I don't like the LED idea. I would suggest a piece of wood molding, maybe 1" or more, painted to match the tile color. If you caulk carefully where the molding overlaps the wavy tile -- so that the small gaps are filled in -- it will look just fine after you paint it.

I cannot address the install question but we have a similar tile in our shower, and we really like it. 3+ years of shopping tile and this is the only one hubs liked. I was apprehensive for the reasons mentioned above but it has not been a problem. It hasn't been difficult to keep clean and only one of us actually squeegees. No one in our house can be bothered to wipe with a towel, lol. Our mastiff gets bathed in it once a week (he has terrible allergies). The shower gets cleaned afterwards w/ a soft sponge and mild dish soap. It only takes a few minutes. No mildew, etc. I agree that you will not like a darker grout. We matched to the tile and it just disappears. You won't lose any of the handmade effect of the tile by matching the grout. Up close our grout varies in thickness due to the nature of the tile edge. Good luck with your project!