I treat the garrote as an exotic weapon that doesn't increase unarmed damage.
Attacking a flat-footed victim halves the number of rounds the character can hold its breath before making checks and gives a +4 bonus on the grappling check to keep the pressure on.
That's probably three times as long as strangulation realistically takes, and is ages long in game terms, since most combats in my experience once they go to melee usually are over in 3 rounds or less.
It works better as an assassination manoeuvre.
This. And this being the case, I'd treat it as a use of the Assassin's death attack.
(Which sucks, because it means that only members of that PrC can effectively use a garrote, and because I don't believe PrCs make sense anyway. But given the way the 3e rules are laid out, this seems to be the best available fit.)
It is very long time in combat, but that's because it is a very poor tactic to attempt in a melee. Even at the more realistic time, it is too long for combat time. It works better as an assassination maneuver.
The goal is to get a set of rules that not only could be used for assassination but work at least as well as other violent attacks, but which are not particularly effective in combat. And in general, I'd like a generic set of strangulation rules so that I can have monsters that attack with strangling attacks and it be relatively balanced.
I don't allow a special Assassin class at my table (and don't allow any PrC for that matter), and I have a general rule called, "Celebrim's playground rule", which states that if you could imagine a five year old attempting to perform the action against another five year old (horrific though that may be in this case), then you are certainly allowed to attempt the action as a PC. You might suck at it, and you might be clumsy at it, but you can try it with at least as much chance of success as the 5 year old. Siloing off 'strangling someone' as a thing that can only be unlocked by a special character is a non-starter.