Daniel:
I don't think you will need a flash meter unless you are doing studio work in a very controlled situation. I just think it would slow you down. Just get any flash (I checked and they stopped making the Metz 32 series) that the size (small) agrees with you, perhaps it can bounce... as long as it has Auto Aperture settings on it.
As to your Nikon SB-600 flash, it should work on your Leica without damaging it. Unless it is so top heavy that somehow it damages the Leica's flash shoe in a freak accident, but probably unlikely. Use the SB-600 in Auto Aperture Flash (AA) mode. Dial in an aperture value on the flash, and it should tell you what distance it covers. You then set this aperture on your lens. Clicking the lens a half stop open will make the flash seem "stronger", clicking it closed a half stop will make the flash seem weaker. The weakest setting the Auto Aperture on the Nikon flash will probably be f4 or f2.8.
The flash will use the Auto Aperture settings (via a sensor on the front of the flash) to properly measure the right light output. So with this, you really wouldn't need a flash meter, unless you are doing controlled studio work.
But if you are set on getting a flash meter/spot meter, Sekonic makes one. They are big and expensive.
As to your M6 meter, it isn't the battery, right? Preferably you are using lithium and not the alkaline/siver oxide LR44 type. Maybe the contacts are dirty.
The beauty about Leica M is keeping things simple. I think a small flash (which you wouldnt be using all the time anyway) would be perfect.
Good luck, Charlie