No, it always used MP. The only change the Ring received is, to my knowledge, the big buff it got in terms of attack power.
Against the rogue magitek troopers I typically fought and killed them - sometimes with great difficulty, but sometimes I was able to just consign them to the void with Alterna. The difficult was maintaining sufficient distance for Death to be effective, which could get pretty nasty in the early hallways. Sometimes I'd just avoid conflict if at all possible, such as with:
Foras, right? Avoiding Foras is much more difficult, but it's a matter of timing more than anything else. Some later parts of the chapter, when it starts presenting some other high end cie'th demons were also pretty harrowing, but the windows for avoiding combat are looser.