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could citrus degreaser (Pedros, water-soluble I think) replace the detergent?
If that's what you have, it's fine. There's nothing special required once you're down to an oil film a few molecules thick, any household or janitorial detergent will do. Make sure you wash thoroughly with plain water to clear residual detergent, as some formulations contain ingredients which won't bake out during the drying stage.
Any solvent degreaser will leave a thin oil film on parts, but it will remove the majority so that the ultrasonic+detergent can get to the final layer of oil molecules and hoover them up.
When I was a boy, white spirit was called turpentine substitute. You won't gain anything by using both, in whichever order. There might be something to be said for washing with alcohol between the first solvent (hydrocarbon types including xylene, "white spirit", various terpene mixes etc.) and the final one (water), because the first solvents are generally immiscible in water but soluble in ethanol. Using alcohol to extract most of the first solvent residue leaves less work for the detergent to do, and residual alcohol dissolves in water.