I also have a record stay set. Out of the four requirements mentioned I would ditch the stay set. It's nice just not a deal breaker and commands higher prices.
Clico and Record (CS88 with the casting fault behind the mouth scraped out) SS here, would opt for SS over RW handles. For irons, the thin laminated CS iron is a dream, otherwise I do like the heavy pre-Garlick O1 from Clico (Mike must be turning in his grave)