My "Holy Grail" of Model 21s is a 16 gauge with double triggers, straight grip, splinter forend and 28 inch barrels weighing no more than 6-3/4 pounds. I've never even seen one that meets all of those requirements and doubt one exists.
In ref to your Holy Grail...
I have several M21's which I use for hunting and clays. One of my 16ga guns is a 1932 POW, splinter, extractor, DT with 30" barrels. It weighs 6lb 11oz. A pachmayr pad was added w/o cutting the original stock which added a few oz.to original 6lb 8oz weight. They do exist, and it's my favorite field gun. The original wood is about as fancy as a North Dakota fence post, but the gun handles terrific.
Everyone has double gun priorities- for some it's great wood, others it's originality, some it's handling. My suggestion is for the OP to determine priorities beyond double triggers and start looking and watching. There are M21's to be found without paying crazy money.
They aren't for everyone, but I sure like them.