This was first proposed by a Yesh Omrim in the Talmidei Rabbeinu Yona in Brachos, but rejected. It next appears in the Chayei Adam, who brings this from the gaon Rabbi Avraham Abbale Pasveller (b. Pasval, 1764, d. Vilna, 1836, for a time contemporary with the Vilner Gaon, who lived from 1720 to 1797,) head of the Beis Din of Vilna. The Mishna Berura rejects this opinion, and even the Chayei Adam calls it "a big chiddush."
Reb Moshe is surprised that the Gaon Reb Abbeli didn't mention the Talmidei Rabbeinu Yona's earlier rejection of this shitta. So Reb Moshe says that the Talmidei R"Y are talking about someone who says the entire weekday Shmoneh Esrei. Reb Abbeli is talking about someone who davenned the correct Rosh Hashanna shmoneh esrei and the only error was saying Keil instead of Melech. Although there is issur melacha at night, and all the laws of yomtov apply, the judgment of Rosh Hashanna does not begin until morning. The concept that saying המלך הקדוש is essential, and that without it you haven't properly davenned shmone esrei, only pertains when Hashem is exercising Malchus through judgment, and judgment does not begin until morning. (He proves this from the Gemara that says that the Beis Din shel Maalah seats itself only when Beis Din shel Mattah is seated.)
As I said before, the Maharil was only talking about making kiddush early, not about davening early, and I'm assuming that this is bcause a person can daven before he is mekabeil yomtov, while Kiddush is a real kabbalas yomtov. (Only according to the Rambam can a person make kiddush without being mekabeil Yomtov, and I believe that's a daas yachid.) But the minhag is to avoid davening maariv early, too, out of concern for the Maharil and in general in order to say Krias Shma in the right time.
So at the minyan I'm making, we're davening maariv after ג' רבעי מיל out of respect for the Maharil and so Krias Shma shouldn't be too early, but we're not waiting an hour, on the basis of Reb Moshe's psak.