unmolested K&T is marginally ok. but tapping into it, modifying it, can add new hazards. a good friend had a small home fire where a solder joint detoriated and overheated, fortunately he cauht it just in time. it was smoldering he could of lost the entire house. his dad had soldered that joint over 30 years ago....

which is why i said just replace the entire thing..... all the 3 way light switches etc, that the OP said he had intentionally miss wired