You seem to understand how I think. I like that. I've been a student of the divergent evolution of Doom ever since I got my first copy--for the SNES. Don't hate, it's almost all I had at the time. When my friend, with the PC version, insisted his was better, I started picking up other versions. Now, when I look at the consoles, PC Doom clones and modding community, I see a complex web of exchanging ideas which has made Doom a game which has experienced seamless evolution through the years...unlike Doom 3, a situation in which they might as well have said "Let's do it all from scratch". Granted, the tech and engine were state-of-the-art...but I'm not feeling the love.
Pretty much everything you mentioned is now moot with source ports -- Doom and 2 are capable of everything Heretic/Hexen are capable of, and beyond, with the right source ports.
However, I understand your basic premise: mix the best of all games. Arguably though it would be hard to do so - the best of Heretic may not fit in Doom (Doom and 2 are carefully balanced in pickups, whereas Heretic relies on random drops and a carryable inventory. Both systems encourage remarkably different playstyles), the best of Hexen may not fit in either (Hexen has a tiny bestiary specifically because it is more of an atmospheric puzzler. Kind of like Zork, in the Doom engine, on crack. Doom's puzzles are puzzling enough at times).
Honestly I think the game stands alone with the features it has. Doom would have been designed differently if id had attempted to place an inventory system, flight, and put-together weapons in it. Then it wouldn't feel like Doom. TBH I have looked at the modding scene for Doom and thought, "What is missing?" and I believe nothing. Not to say there aren't more ways to innovate. But I think improving on the original Doom formula is unnecessary.
There are supposedly some Heretic mods (HPack and the community mod in the thread in WADs) that will improve the game - that game does need improving. And Hexen could do with a beefed up bestiary, without getting ridiculous (but as for a version without puzzles, the Hexen expansion by id is a good example of what that would be like), and perhaps an improved weapons system (both Heretic and Hexen have a "snowball" style weapon balance, where later weapons are stronger than earlier weapons. Hexen compounds the problem with this balance by introducing exponential same ammo use, to the point where if you use your ultimate weapon you waste your other weapons and have to go back to your base).
So in conclusion I don't think Doom needs anything specific from the modders - just more of the same awesomeness that they continually put out. I don't think there is some hidden holy grail formula of change that would suddenly blast off and be amazing. But I do think Heretic and Hexen could both stand to see some "completionist" improvements - bestiary and weapons enhancements that keep within the flavor of the original game while bringing it to the same gameplay depth as Doom. They don't feel as versatile as their predecessor to be very certain, even though they have awesome things like flying and an inventory. But when you look at the theory behind the items and the weapons you can see that the items are good precisely because the weapons lack variety. They do not deepen gameplay other than making it harder for mappers to plan how players could react.