If this site could have only one time control...

I think it should be G/120 days. Agree? Disagree?

What do you mean by "G"? It is "Game"?

That would mean a game against an unresponsive opponent would time out after 120 days+vacation, which is a lot longer than the 10 days+vacation that we have now.

Disagree. You would need to make multiple moves per day to finish a 19x19 go game, but you could dawdle for weeks in a 13x13 hex or dots and boxes game.

Yes G=Game

You actually mean 120 days, not 120 hours?

I like the time control we have today very much, and would not wish to alter it.

If you mean that all games should last 120 days(or shorter) then sorry but this is one of most stupid ideas what I read in this site.
1. Time zone unfairness is even bigger(player with time zone western than opponent have advantage).
2. As mentioned some games are longer some are shorter. How you imagine 120 days for both "polyomino mini" and "GO 37x37".
3. For games with strict number of moves like Reversi this is just unnecessary complication. To really know how much time you have you must do calculation for every game (MaxMoves-MovesPlayed)/TimeRemaining.
4. In other games like every GO games, or drawish chess games you can only play without pass or draw acceptance. For GO it's disaster.
I don't like "Sudden Death" time control even in real time games, because this aim to blitzing. For correspondence games this will aim to sleepless MMORPG/MMOSG-like games.

I would much prefer a system with byi-yomi (also known as grace time) where each move gives you a certain amount of time (not cumulative) and if you use that up, you start drawing from a reserve pool (not restorable).

Sadly it's not byo-yomi(It is but reverse to be strict), because I prefer this much better than "normal" byo-yomi, which it's used in GO. This system it's called bronstein time.
It's good time system but fischer it's probably objective better. Suppose you want some free time. Some of your games will have reduced reserve. Then suppose you want some free time again after few months, but this will not be easy because of your old games. In this case you need to be available practically every day(not counting vacation) to play at least old games.