I would say your problem will only get worse by going to a thinner oil. Take the clutch plate steels out & polish them up, so they're nice & smooth. That should help. Also check the gear shift drum selector. I've seen that thin steel plate on the end bent up/mangled from bike being dropped on LH side. I discovered this when rebuilding my K2 project. Won't shift real good like that!
Polish the steel plates, really?
I let my shop glass blast mine just a litlle for grip since I had some slippage back in the 80's. They still work fine with my existing cheap Cruzinimage chinese fibers.
I'm currently having 10-40 mineral oil in now due to break-in new pistons/cylinder. Clucth work fine, only the typical problem to find neautral when engine is warm and running. Off and the neutral will easy slip in.
The oil in now has only been used 160km (100miles). About 850km more and I'll change to 20W-50 mineral, same model, Motul 4100. I'll see how that will feel.
If neutral will still be difficult to find, I'll change earlier to my 20W-50 synth oil that is waiting for entering the engine that I know work fine clutch wise and neutral. Synth is not recommended for breake-in.
I'll try Motul 5100 15W-50 semi-synth in my K2 when I have assembled it and it has been broken in with 4100. It's currently a project in pieces on the floor, shelves, paper bags, boxes, Honda labeled bags, Yamiya boxes and David silver boxes.....