Re: female mayfly
Honestly I think presentation, size, and shade (light medium dark) would be most important, followed by profile then color.
If I had those bases covered and still wasn't hooking up on top, I'd switch to an emerger.
I have tried egg cases on some may and caddis dries, orange egg dubbing things in the middle of scuds, and even orange heads on BWO's and other mays to imitate the large eyes of males. Made me feel great when it worked, but can't honestly say it made "the" difference. Most likely blind luck at least in my case.
That being said, I do believe there are certain triggers, perhaps known only to trout, that can make a difference, and if mays are dipping to drop eggs, maybe that's one of them. It'll be interesting to hear from others on this. Good question.