Another vote for the scraper method. It seems to work better than degreaser type cleaning products. Mine is just a regular one with a changeable razor.
My local AGA shop ran a free session in the summer (when most AGAs are switched off) which gave advice on how to clean them, and flog their branded cleaning products with 20% off.
It was quite useful. It's definitely easier to clean whilst off and they told us never to use 'power spray' type products as they will damage the enamel surfaces and it's irreversible.
Don't bother with their branded cleaners though, the paste is the same a Astonish and the e-cloths are just regular e-cloths but more expensive!
The domes can be cleaned with car chrome polish on the outside and with a Brillo pad on the inside. Those circular pads hide a multitude and prevent further damage.
The hot plates need a regular scrubbing with a wire brush (when it's switched on) to get rid of burnt on deposits, there needs to be a good unobstructed contact between the plate and the bottom of the pan.
If you take the doors off, make sure you don't fully submerge them in water when soaking them, it ruins the insulation inside. Just soak the raised inside bit in shallow water instead.
The inside of the ovens an mostly self cleaning. Deposits are burnt in the heat and mostly carried away by the flue. I occasionally vac in there. Leave the doors open for a few minutes to let the heat die back a bit then put the metal nozzle of the Henry vacuum cleaner quickly round.
Also, keep the control panel free of dust (it gathers quite quickly with the heat) as the whole thing works more efficiently without dust.
HTH!