When mine die I will happily replace hem with Yamaha's newer powered versions. Reports on reviews are they sound very close to the originals. I myself would not repair them as that money would be better spent on new equipment. Monitors are sort of the heart of your studio and not a place I would want to compromise. It's also getting hard to find appropriate power to drive them. Good power amps are more than the cost of powered speaker pairs. Huge advantages to powered speaker. 
 
I rebuilt my 30 year old Tannoy 6.5 monitors with parts from a discount speaker suppliers here in Canada. It cost me well under $80 and they are like new and sound great once again. It was easy because Tannoy had used commonly available speakers.  But Nsm 10's have a special white paper cone and there is no direct replacement as a result of that paper no longer being available,. Therefore any re building, I would guess, is not going to result in having the same sound anymore, so what's the point. Without the original speakers it's just a box. 

Even if brand new replacement woofers were available they wouldn't sound like the original ones. Speaker cones soften with age and use and after a few years heavy usage can sound very different to when they were new. As I found out when I replaced a Jensen C10 that had been in a guitar amp for around ten years and had started to come unglued. The replacement was much tighter and brighter than the one it replaced, sounded like a different amp.

On the plus side the crossovers are probably OK, takes a lot to damage a crossover, but may have been designed for the frequency characteristics of the original and now unavailable cones so how well they'd work with anything else is a bit of a gamble. I say 'may' because the NS-10 was hardly designed with critical studio use in mind but as a not particularly expensive hi-fi speaker.

Me, I'd look for a pair of active monitors and maybe consider reconing one NS-10 or seeing if one working speaker can be made by cannibalising the pair, and consider using it as a mono mid-range checker.

Thanks for all the input, I was naturally in a state of panic the day of and after. I have in fact combined the parts to have one working speaker and have a used tweeter and re-cone kit on the way. I also am seriously shopping for a new approach to monitoring.  If the two NS 10s end up sounding significantly different I do like the idea of using one for mono checks. Or perhaps putting them both on the tv.
 
We go forward :)