Borrowing from others' ideas, I offer the following scenario (it's not foolproof, I'm just thinking out loud):
On the evening of the 23rd, DA picks up TT from bowling, and they go to the house to pick up the spare car keys, etc. The police have said they'll be out to the mall at 11:00pm, after it closes. I don't know what occurs next in that time frame, but I'm going to assume maybe it takes TT a minute to find the spare keys to the Olds, and he has to make arrangements for ST to pick up Shawn from the bowling alley.Then maybe TT and DA sit and talk, to pass the time. DA is worried, because it's not like Rachel to do this sort of thing. Maybe she's reluctant to face the other families because it's her sister who was "in charge" of this outing and now they're all missing. TT is remembering the fight at the bowling alley the previous night, maybe thinking of other guys he's seen or heard of Rachel flirting with. Maybe Rachel has run off, or met up with someone else. Maybe he's questioning the whole "marriage thing".
At any rate, he and DA show up at SS at around 11:00pm. The other families are there, and are understandably upset, panicked. The car's been found, locked up, with absolutely no sign of the girls.
TT's got the spare keys, and they search the car. There are police radios and dialogue between officers/dispatch. TT needs his car back, and needs to calm the families (including the A family). He and DA are dismissed by LE to go home and wait by the phone. He and DA head back to Minot. Later that morning, TT writes or finishes/edits the note, puts in his pocket, then proceeds to go out to the mailbox. He comes back with the note, shows it to DA. They take it to her folks, police are called, come collect the note, and ask about the envelope (oops). Sometime later that day, he's told he can come claim his car. So DA takes him to pick it up. On the way home, he stops at the SS mail kiosk and picks up a postmarked envelope, addresses it, seals and tears off the flap (thus making it appear to have been mailed containing a note), before it is delivered to LE.
I know this was a long read, but it's the only scenario (involving TT) that really makes any sense to me. If this doesn't work, I'm going to suggest maybe TT didn't do it. Feel free to correct any inaccuracies.