The standard advice here is yes, just leave it on for the entire yomtov. Sorry, we're not magicians here that can hey presto improve on the wheel, so to speak.
If you really, really wanted to put it on a time switch (/grumble/), I suppose you could, though that would have your oven clock blinking all sorts of funny times throughout yomtov; you'd have to find one that can handle enough current for your range; and the truth is, Rabbi Moshe Feinstein wasn't crazy about the timers anyhow -- he accepted using them for lights (their #1 application), but not anything else.
Hinting to a non-Jew -- bad idea. If something came up, e.g. you forgot to turn the oven on before yomtov, fine you could try it. But to try and rely on that in the first place -- and then hope that you can do the hinting within the bounds of halacha, while getting the non-Jew to turn the element up/down, on/off just the way you want it, without driving him crazy -- just a bad idea.