I don't have the M/Lee instructions handy,,but I'd avoid boiling and detergent solution and placing the steel parts in it.
Take it up to just under boiling temp,,just under 200F is fine.
At boil temp, SOME detergents will lightly etch, leave patchy areas of discoloration or a coating of residue on the steel.
Perhaps the additives in some are the problems (perfumes, colorations, softeners,,ect)
Even the commercial cleaner Brownells sells (sold?) was used at 195F.
I know from experience that if used at a rolling boil, it would leave patches of off color etching on the bbls.
I use TriSodium Phosphate cleaner. It's about as pure a cleaner in water solution as you can get.
It's still available but you have to look for it in DYI stores and the like. Usually in the paint & prep area.
All the cleaning agents that the pretty bottled stuff have left out.
The hot-soapy water idea is a good cleaner when used with a scrub down to loosen the crud. The old standby laundry brush works well for large areas,,toothbrushes and M-16 cleaning brushes for the small areas.
A hot water rinse, same scrub down,,then a cold water rinse.
If you don't use the cold water rinse, the parts will start to flash rust on their own. You may not want that to occur. You deffinetly do not want to apply some cold rust blue solutions when the metal is warm/hot. Most of all Laural Mtn. It will deposit a nice coating of copper for you on the warm metal.
If you're using M/Lee Express Rust solution, going from the hot rinse right to the first coating of solution may be possible if the metal is hot enough.