John S,
Thank you for your sympathy but your problem is much more serious than mine. My hub slips occasionally in 4th but you're only able to ride in one gear. I'm not surprised you are thinking of giving up. On Roadster's advice I tried that Jagwire cable, but as Brucey says if you have a good quality cable and it still slips, the lubrication is probably more important. I've got a new Shimano cable ready to install. Also, here's a quote from Brucey:
NB with CJ-8S20 especially, it is absolutely imperative that you use the correct (metal) ferrule at the cassette joint end of the housing. The ferrule is supported on two small projections and plastic ones can just fail. The shimano cable (which comes with 8s shifters) has an aluminium ferrule that is crimped onto the cable housing. A loose metal ferrule will work but the cable housing can pop out the ferrule which throws the indexing off.]
I recently changed the Revoshifter on my bike and the new one came with a new cable and housing with the correct ferrule. But due to the internal cabling on my bike I had to cut the housing. I'm now going to follow the advice I have received earlier in this thread to route my cable/housing externally in a continuous run. But I will not be able to re-use the original housing as I have cut it. I doubt whether the housing is available separately from the shifter, but someone else may know better.
Regarding belt drive, I considered that two years ago but decided on a chain because the belt drive version was £200 more expensive and the belts are expensive to replace. But it is a lot lighter as the weight of this bike is a big drawback for me. I don't think I'd have much choice now as most of the new hub gear bikes seem to come with belts. You need a special type of frame for a belt, and I don't think it would solve your problem.
My hunch is that both our problems are caused by cables, but having said that the fact that your hub slips in so many gears does suggest an internal problem with the hub. But like you, I'm not very technically proficient and would not be confident enough to open up a hub. Here's another quote from Brucey:
There are hundreds of thousands of bikes fitted with N8 hubs and revoshifts which don't give this sort of trouble. Whatever fault you have I would expect someone reasonably competent to be able to fix it without too much difficulty. You may be frustrated but buying a new bike is something of an overreaction to this sort of problem.
The problem is in finding a decent bike shop. Last November I fell off my bike and bent the front rim and broke the brake lever and the gear shifter. I took the bike back to the shop I bought it from. I had a broken wrist so was not in a hurry. I went back after Christmas and was told that they were unable to source a replacement Revoshifter from their supplier until mid-February. On 27 Feb they rang me to say they still couldn't get it, so I went and collected the bike. The good news was that they had done a good job of re-building a new rim around my Shimano dynamo hub. The bad news was that they had fitted a
silver brake lever in place of the original black one, and they had not set up the pads correctly.
It took me three days to order and receive a new Revoshifter from SJS Cycles in Somerset.
Needless to say I shall not be returning to that shop. Good luck with sorting out your problem.