From what I’ve read on here the zephyr s clutch is the same as my kz750,but better,not sure why.
If I were you I would get her running hot,drain the oil and the filter of oil,if it’s clean oil put the filter back in and try some 10w/40 semi synthetic. It could just be the wrong weight and a lot cheaper and waaaaaay easier than changing the s clutch. And you can always drain it into a clean container for re-use after you’ve changed the s clutch,if needs be.
You can do it with a manual but you’re gonna need some tools you may not have. For starters you will need a clutch holding tool,one of the mole grip types is fine,and you could do with an impact gun to get your clutch hub nut off easily. It can be done with a breaker bar and a length of tube over the end or a flywheel strap but it’s a faff. Oh,it’s soooooo much easier on a bike lift,invest now if you don’t own one,really,I bought a 2nd hand one for £200 and it’s my best tool.
You can follow the instructions in the manual,it’s pretty basic stuff,just a lot of work removing exhaust,footpegs,engine covers,clutch etc. Once you’ve got it all off and the sump is removed it’s fairly easy to slide the secondary shaft through to the rhs and jiggle the s clutch and gear out together. After you’ve done it you will realise it’s not hard, Just time consuming.
Top tip, there’s some staked screws on a retainer plate you will come across and have to remove,make sure you have the correct screwdriver bit to undo them. You usually get a selection in a decent socket set and from memory it’s a pz3 or something, you will know coz it fits like a glove and doesn’t ruin the screw,lol.
You need to remove the secondary shaft nut on the lhs under the blanking cover or certainly loosen it before removing the clutch assembly. If not that’s where the flywheel tool comes in.