Man of Honour
The cassette on my bike is a Shimano HG20-9 11-34, 9 speed, could I replace it with a Shimano HG300 9 Speed Cassette 11-32T?
That looks nasty.
4 years though, i'm not sure I've ever had a tyre 4 years!
H end stop set up right? With the cable not clamped down, and using your left hand, pushng and letting go of the rear mech whilst pedalling does it fall back to smallest, and push up to largest, and neither case go to far and derail onto spokes or between frame?
Slipping as in the chain slips on the cassette teeth or its trying to go up/down a cog and isn't getting there? Always in a certain gear or across the range?
Definitely the chain/cassette and not the freehub slipping?
Check if the mech hanger isn't bent. At at H end stop position, it's a straight line between the sprocket and jockey wheels.
I'd replace inners and outers for the rear derailleur. Or at least blast GT-85 down the outers and see how freely a inner cable moves back and forth through each outer section.
Your chain could also well be causing this. Have you checked link wear on it?