FWIS3

Still deciding on the best way to tackle this job. The lounge had carpet and the kitchen dinning area was originally tiled, with wall tiles.
I changed these last year to proper floor tiles as too many had broken, because they were thin wall tiles and not meant to b walked on.
The kitchen and the dinning area was divided by a bench, cupboards and the closest end to the lounge has a wall that goes up to the ceiling and is a bit wider than the kitchen bench itself. When the carpet came out there was no tile on that area it. It's wall and trim.
From the top the kitchen dinning area looks a U shape with the ends of the U being tile into the lounge room.

The problem is, between the builder that didn't make the wall straight and me going around the bench, created a little bit of error.
So when I measure from the far end, I got the tiles exactly 1 foot apart including grout, but this got skewed a little at the end of the bench so that when the tiles got back to the kitchen entrance from the lounge they didn't follow the original 1 foot spacing from the far wall. They are out by just over 1/4 inch. The spacing between them however is still exactly one foot.
This wouldn't have been an issue with the original carpet, in fact no one could really notice the 1/4 inch offset in 5 feet of blank wall.
But now we are tiling the whole lounge so it's going to be noticeable because the lounge will have continuous tile so no break to cover it up.

This of course would be pretty easy to resolve on its own but the reason I found this error was because whoever laid down the floor had no idea what a level is.
In some places the line is so bad it's out by 1/2 an inch in two feet, that's after me planing away 1/4 inch to reduce the peak.
The way to fix this and make a level floor is to put down a mosaic (mozaic in the USA?) pattern that has tiles about 6 feet apart and each tile is height adjusted individually to make sure that that it sits at the right height in the horizontal plane. But, I can't do that easily because I can't use the simple 3,4,5, right angled triangle trick since the tiles don't follow the 1 foot spacing all the way and that means placing individual tiles in free space and expecting them to line up with the pattern is not going to work.

The other option is string lining but I'd have so many lines that maintaining the right heights would be a nightmare.
My current thinking is a combination of string line, chalk line and the 7 foot level to make a really close layout and just deal wing it.

That's my fun for this week.

Why not just level the floor? Some plywood added to the subfloor....

It would raise it above the tiles in the kitchen.
Right now the tiles in the kitchen are sitting on 1/4 ply on top of the floor plus about 1/4 of tile cement.
Even at that 1/2 inch height higher it was still lower than the high spots. Yeah, it's that bad.
So I planed down 1/4 inch of the highs, just enough so the tile sitting on it with no cement is the right height.

Yesterday I laid out a pattern so I can pick key tiles to glue in place. Basically all the high spots.
I glued down 7 tiles at the right height for the floor to be level.
Now I have to add tiles with varying thickness cement, or glue if it's too thin, so that they all come out to the level of these key tiles.
Means I'll be mixing cement and using glue at the same time. With some tile both on the one tile.

The alternative was to rip out the whole kitchen and lay it out an extra 1/4 inch thicker. That just ain't happening.
At least this way it'll look level.