John -
True about being wired directly, but there are two reasons that I said to check closer to the stator. The first is that it's not uncommon for folks to not clean enough wire in replacing connectors, leaving a high resistance. This would fit with the out of spec found. Second was to visually look for dark areas, indicative of stator damage.
Good reference that I've posted before. You are on page 2:
http://www.electrosport.com/media/pdf/fault-finding-diagram.pdf
Trevor / All -
Getting back to basics, there are really only 4 pieces in the charging system of these bikes. The alternator, regulator, battery, and wiring. I'll add that t's very easy to be inaccurate making measurements at low resistance, too. So addressing each:
WIRING: Since it's cheap and good husbandry anyway, I'd still start by making sure the wiring is OK and each of the connections are truly clean and intact. Inspect the terminals for darkening. As mentioned, it's easy to not cut far enough back in replacing splices and keep copper with an oxidized surface, or to have it cooked in more than one location. Since this connector got that hot, the spades in the regulator plug could also have cooked. Pull each end of the harness, look closely at the pins themselves, and measure to make sure you have truly low resistance through each wire circuit. Do it at the fuse too, and it'd be a cheap precaution to replace the fuse.
ALTERNATOR (Yamaha calls it an AC magneto): You still need to get the resistance from each wire to the engine case (ground). I checked the mx manual and the numbers John gave were right, so what you reported is nearly double the allowable and the manual is clear that the stator should be replaced for this. The alternator is simply a permanent magnet spinning between the three coils and doing so creates an output voltage. Usually, they fail by heat breaking down the insulation in the coils so one or more of them go low in resistance. It's unusual to go high in resistance, but this is the source of all the power which burned out that one connector and melted the old regulator. My guess is that you will end up replacing it.
REGULATOR/RECTIFIER: You replaced it, but it's certainly possible to get a bad reg on the used market. In the old days you could find values for checking the reg by going pin to pin, but our manual has no data like this. Unless somebody has their reg unplugged and can provide numbers, and with your bike in question, the only real way to know would be to plug the regulator into another bike and see if it allows 14 V at 5000 rpm.
BATTERY: Replaced recently, but you could swap it to another bike to see if the battery has an internal short.
Let us know what you find.
Bob / CW