Rita

One diagnostic worth knowing: if shifting under moderate load feels crunchy or hesitant on your bike, that is usually indexing or a worn chain rather than technique.

A correctly adjusted drivetrain with a chain that is not stretched shifts under reasonable load with a clean click. If yours does not, you will get blamed for the technique when the actual fix is a cable tension adjustment and a chain measurement — both of which take minutes.

For the caked-on stuff that the cloth will not shift, the escalation ladder that works:

• Warm soapy water and a stiff brush first. A lot of what looks permanent is just wet-weather road film and comes off with detergent.
• A green scouring pad, dry, for the black glaze. This is safe on an aluminium braking surface and is what most shops reach for. It takes seconds and leaves the track visibly bright.
• Fine abrasive only if there is a real ridge of built-up material. Rare, and if you are doing this often something else is wrong.

Never use a scouring pad or any abrasive on a carbon rim — the braking surface there is a resin layer and you will destroy it. That is the one hard rule in this whole job.

One under-mentioned factor: a single ring puts the chain at a severe angle at both ends of the cassette, and severe cross-chaining costs efficiency and wear.

With two rings the chain spends most of its life reasonably straight, because you are expected to change ring as you move across the cassette. That is a real if unglamorous argument for keeping the front mechanism on a bike ridden for long distances.