new to the party... as most here know I am a total noob BUT I am a master at fixing/hiding ballsup's, there are basically only 3 things you can ever do, only 3
When I saw this I automatically thought of the massive vandalism scratch I had done to my car, as it's a black car I am also resigned to scratches being so visible no matter how small, it is like acid to my eye, your tile floor reminded me of that, a flowery pattern floor is like trying to hide a scratch on a pristine bonnet.
So Let's break it down (as I said this depends on a lot of things)
1> Replace
2> Repair
3> Hide
1> Replace:
Only 100% way that your eye is not drawn to anything is to replace, period end of story, (or in my case repaint the bonnet

) you mentioned asbestos and not wanting to do the work involved or time or something, ATEOTD 100% fix is replace , replace the tiles, replace the 2 or 3 tiles or how many with like for like, THAT IS IT, no come backs
1a> Replace 2: (kinda)
Re:Tiling over the old tiling, you don't want asbestos to come through fine, put some stuff over it, if its Lino, roll another lino over it, if it's tile you can tile over it, I've seen backsplashes retiled, you can do it, how easy or hardwearing is another matter
1b> Replace 3: (kinda)
Take a picture, or get a hand scanner and scan it into a computer, print it on flexible plastic card, or even TSHIRT paper, then print it out cut it to size and using a clear contact cement paste the 3 or 4 tiles, you could use tshirt to hot iron to the tile (it is very difficult, take your time but it is possible and it is VERY hard wearing
2> Repair:
I think most of the usual things have been said, but you could try, getting some clear PPF and see if it makes it LESS obvious, the black is from the dirt so you need to clean it out
3> Hide:
There are so many ways to do this, this is the art of deflection, some ideas
- Decals
- Paint some of the tiles to make a pattern
- PUT SOMETHING ON IT LOL - chair, fridge, box, cat,
- Can you put a transition tread from one side to the other
- Paint the whole flor
- Epoxy the whole floor
I can give you more ideas but I'm looking at an enlarged pic of 3 tiles, is it just you who's seeing it, is it really noticeable from say standing position.
please take several pics, different views of the whole room and from a standing position, it could all just be in your head
Now as I said, I'm just a humble home tryer (not even a home diyer) I try pretty much everyone on this board has more experience, more sense and more professional than me, so please do feel free to ignore the above, but as I said I keep seeing the line in my car paint than even after a 4 stage machine poilish burns my eyeballs, no-one else really sees except me