I recently acquired a 2000 speed triple. Love the bike except finding neutral when cold. Once it has been put into 1st gear, with a nice clunk, it doesnt want to come out. I've adjusted the clutch and changed the oil. Shifting between gears while moving is fine except for 2nd to 1st and 1st to 2nd occasionally it's a little clunky. Once the bike has been run down the road a little ways finding neutral is easy. I suspect the bike has sat for a while. It was found in the back corner of a garage covered in dust. Any input is appreciated.
Sounds like you clutch is dragging a little. If you can take a little more slack out of the cable without it being too tight that will help. Also, what weight oil are you running? A lighter weight might improve it when cold. I don't know what's recommended for the 2000's. My '06 OM specs either 10W40 or 15W50, I always run then 10W40.