That is pretty much what I would do, too - always cut the knot out. Also, how to deal with ends depends on what kind of yarn you are using. If it is wool, you can 'felt join' them together. wet them just a bit and rub them together between your fingers - they will felt enough to hold them together. Other yarns, depending on the bulk, I might hold them together for 3-5 stitches, leaving tails long enough to weave in later. Or you can just drop the 1st one and pick up the 2nd end for the next stitch. If I'm not knitting in the round, I may want to work the join at the edge.
I'm not sure there's any advantage to re-winding. I still need to know where in the project the knot is going to fall to help me decide what to do with the 2 ends. If it's a sweater project and the knot falls in the arm pit area, I'm not going to stress nearly as much as if it falls right smack dab in the middle of my bussum.