I think the only people that get stuck at the Mongol border for hours are the mongol rally people, who have issues that you won't (ie, they are leaving their vehicles there).
But also note that at least some of the boder crossing into Mongolia are closed on weekends--so either triple check about the khyakta crossing or arrive during the week. IIRC when I looked at this issue a few years ago, that border point is open on weekends, but I'm not 100% sure.
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