I know the first player being able to end the game with a sure win is a strong thing, that's what I am trying to counter.
I'm saying that ANY player being able to end the game with a sure win is a very strong thing. Your suggestion gives this very potent advantage, which is normally available to all players, to only one player.
With rules-as-written endgame rules, everyone is playing the same game. The way to win the game is to end the game, on your turn, when you have more points than all the other players. With your suggested endgame rules, now you as first play and I as last player are playing different games. I, as last player, am playing the game from before; I want to make the game end on my turn, as long as I have more points than you do. It doesn't matter whether I have 1 more point or a dozen. You, as first player however, are playing a very different game. If you ever want to win, you have to trigger the game end (I obviously would never do so unless I had more points). However, you can't just trigger the game end when you have a greater score than I do; you have to trigger it with enough extra score to outlast any points I can generate on my last turn
with me having the knowledge that it's my last turn. I can trash all my Mining Villages, Bishop my Gold freely, Apprentice my Possessions, whatever; I know that no matter what I do to my deck, it won't matter, as long as I get enough points to beat you right now.
Player 1 will never get that opportunity. If you as player 1 go all out one turn, trash all your Mining Villages, etc., but don't actually pay the cost of triggering the endgame, then I can just... not end the game on my turn? I can build my deck instead, score some points, but not trigger the endgame either. I never have to end the game except when it will guarantee me the win, but you do have to, or you can never actually win the game.
I certainly don't disagree that going first is an advantage, and going last in a 4 player game is a large handicap. I also recognize that the vast majority of my Dominion has been 2 player games. I have played with this variant in a 4 player game or two, though, and I know what I personally dislike about it. Clearly our opinions differ, and that's okay with me. I certainly don't want this to look like some sort of vendetta or anything.