The last thing I would start with is replacing the master cylinder. Change the fluid. Do an oil change on the bike (if you already did, check the oil for the right mc type).
You start by asking here. I also thought rivets on the clutch, but haven't followed the systems enough to know if you are having the same signs.
But the oil change is easier and cheaper first.
The rebuild of the master cylinder will be phase 2 of the process. Flushing with fresh fluid will be step one. I use full synthetic DOT 4 fluid, have for 141,000 miles now.
Engine oil was new/fresh when I put it up last fall (including filter). I'm not concerned whether it's the right oil... same M/C specific synthetic oil I've been using for 141,000 miles now.