ariallito's answer seems to cover your needs. Just want to point out that unfortunately there's no 100% private match. Even for unlisted matches, after it starts, the game will be visible in the started/active list in the landing page, and also on your profile.

Agreed, recovering 1 minute up to 10m allows for way too long games, considering this is the fastest/shortest option.
I'd love to pick a custom time, I wonder why this isn't possible. I mean, the server isn't supposed to trust the clients anyway, so validation is (hopefully) already done. So we'd be able to choose any value in a reasonable range (to avoid absurd durations like 1 second or 2^32-1, etc).