So if your materials have a tendency to vary like that, this is what you're going to need to do with the next batch (pardon if you're already planning this, ha, or if I already wrote this in your thread). Arrange to spend some time with the next delivery before the tile guys get to it. You might want to order extra, based on the potential range of variance in the material. You go through every box, every tile, and set aside (as in: hide) any tile you cannot live with. This is why you might want extra. The fussier you want to be, the more extra you get. Then physically place all the tile where you want it. (Or talk the tile guy into doing so, with you managing that, if you can't do this yourself.) Arrange the tiles to fit your aesthetic sense. Arrange the subtle color differences to your liking, so that no odd patterns or blocks of colors emerge. Place borderline tiles (because of color or finish) on the side or end of the pool where they'll be least noticeable. Conversely, put the "specials" in a location where you'll be able to admire them. All this done before the first one gets mortared in.
Discuss with the installer how you want the miters to go. It may end up you have to have a partial-length tile somewhere. If they won't shave each tile so that doesn't have to happen, then decide where that odd one is going to go (usually in the middle of the run, but I'd push for shaving tiles to eliminate it). Be prepared for a discussion about an up-charge. That wouldn't be unreasonable if your level of pickiness is costing them a lot of extra labor hours.
There's even the possibility that the PB and/or the tile guy will appreciate this extra effort from you, because it will alleviate from them the responsibility of pleasing you and having to do work twice. I placed my own step markers when I had them redone. I rejected a bunch, and sat on the deck as the tile guy tried them out position-wise, and gave him a yay or nay for each piece. I got a sense he was just as happy letting me make the decisions, but frankly, I wouldn't have cared if he wasn't.