An interesting topic notwithstanding it has been all previously covered but I suspect we all modify our approach based on our own experience.
For example I have almost completely moved away from using a tumbler and ultrasonic cleaner. The results, for me at least, were not forthcoming.
On metal parts I first use a 12L parts cleaner with water soluble concentrate to remove grease & grime and then if needed and irrespective of rust soak in Evaporust. I find this product restores the plating finishes to their original sheen. Naturally any rust is removed most effectively.
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On small metal parts I use a combination of a wire brush on a bench grinder or, for example, in the case of jones plugs (male & female) a wire brush within a dremel tool.
For plastic parts, mainly posts, I use dishwashing detergent in the sink!
dhutton it seems that the oxidation on your machine is fairly severe and to be most effective a fair degree of disassembly will be required. But it is surprising how quickly you can move through it and the results will give wonderful personal payback.