For the wires pulling away from each other: try twisting more times before you fold the NR wire back and wrap, and make sure they're actually twisting together. I had that problem a few times where I'd get done twisting and only have like two twists . . . I guess the wires were just slipping through my fingers instead of actually twisting together. Practice makes perfect ;-)
As for the high resistance issue: this may be a really dumb question, but you didn't accidentally use two lengths of resistance wire, did you? That's the first thing that came to mind. Based on the total length of wire used and your final resistance, it sounds like a plausible explanation. I'd check your wires with a multimeter just to make sure. The NR wires should give you virtually no ohms reading (other than the meter's internal resistance)