Well done at last you got it sorted out that is the main thing.
Now it is not surprising how and what can go wrong by swapping wires, if you take each switch it has 3 terminals com, L1 and L2, and 3 wires, this alone can give you 6 permutations, combine that with 6 permutations of the other switch you get 36 different combinations, that can produce many different patterns, albeit some patters will be repeated and exactly the same.
going by Bernards corrected diagram,
It was correct as a two way circuit to begin with,. I modified it to be as you described the change which meant it was no longer a two way circuit but simply two switchs in parallel. Either switch down would put the light on
up up OFF
up down ON
down up ON
down down ON
Bernard, thats right, I wanted you to redraw your diagram such that it replicated the above logical states, (The logical states of his present problem) and that is why I asked you to do that, hence I called it corrected version to replicate his present fault situation, to see how far adrift his wiring might have been, but by all means this didn't imply that it is how a 2 way circuit should be.
If you now consider we have 3 terminals in each switch, and 3 wires in each switch, this can give you a combination of 6 permutations within one switch, so when you multiply that by 6 permutations in the other switch you have a total of 36 permutations though some of these will result in repeat pattern or logic, but connections wise you have 34 ways in which one can wire the two way switch wrongly, there are two or may be three ways you can wire it correctly.