I've used the Taylor method for years with hex core strings. Works great and never had a problem. With round core strings, DR Rare, Pyramid, Newtone MCs etc, You do need to modify the procedure a little.
Instead of cutting the wound strings at the next tuning peg, bend the string at a 90 degree angle where you would normaly cut. When installing the string in the post, just bring the bend flush with the hole at a 90 degree angle. BTW, I usually add one more bend to the excess part of the string. This ensures that the winding does not loosen from the core causing problems with tuning, intonation, dead strings etc. Round cores, without the hex, does not give the winding a sharp edge to cut into to hold the winding in place. The bend holds it in place. Once the string is up to tension, it's safe to cut it.
I've only had problems with round cores once and that was early on when I started using them and forgot to do the bend. Has worked for me for the past three years using roundcores exclusively. I have never had tuning or intonation problems with rounds and believe most complaints about them arise from improper installation methods.