Baskets easy enough to replace but don’t expect the centre clutch nut to come off easily … you’ll need a clutch holding tool and an air gun will make your life easier.
Could also be warped clutch (plain / drive) plates. Worn cush drive rubbers (rear wheel) will also make the problem feel much worse. Kawasaki gearboxes have always been a little ‘clunky’ right back to 1972 it’s more annoying than an actual problem.
Slackening your clutch cable means the clutch will disengage less rather than more. Not enough freeplay in the cable will result in the clutch slipping rather than dragging.
What oil did you use and (sorry about this) did you put the right amount in? Don’t assume just because it says 3.6l or whatever on the side you will have to put this much in … check you haven’t overfilled it slightly, it wouldn’t take much to make a difference when the things still cold.