The dynamo should not be giving the readings that you suggest. My first course of action would be to remove the brush cover band and at least check that that the brushes are free in the holders with suitable spring tension and that there are no trapped wires.
I scratched out any muck on the groves of the commutator with a sharp small nail/pin. I replaced the brushes and springs (from memory you have to be careful when ordering the brushes as I think that there are two types of dynamo; a short one 40w and a long one 60w).
If you are careful, get the bike running, take off the strap at the front of the dynamo (looking at the bike nearside). Remove the "bakelite" brush cover (single screw in the middle of the dynamo). Expose the end of the commutator and spray with WD40 (I tried electrical cleaner, but it seemed to leave a deposit that didn't help).
Then do your multimeter tests at the dynamo i.e. checking that you get a steady increase is DC voltage as you increase revs (I can't remember what my dynamo belts out, but it is well over 12V on not too much above idle) . Then check at the battery to ensure that the voltage is steady and greater than 6V.
If this all works fine, I would put in a switch that isolates the battery i.e. you switch it off when you park the bike up.