I'm from Missouri, in Missouri, and I can tell you this right now: any suggestion of a title through another state is now outdated BS. The last state in the Union that allowed that was Vermont, which I used on a couple motorcycles three years ago, and they've closed that loophole. You can get license plates in several other states but NOT TITLES.
Every state is in NMVTIS now and there's no pulling that wool over the states' eyes. The feds put an end to that. It is actually against the law to purchase a vehicle with NO title, in Missouri.
A bill of sale doesn't mean squat in this state, unless you're filing for "gift" status to avoid paying taxes. Those have to be notarized.
That said, you have a couple options for title. A dealer can buy a vehicle with no title IF that dealer can prove that the person selling is the last registered owner. They then file for lost title and apply for new title when it comes in. You MUST be a dealer to do this.
Or....
Missouri itself finally started to offer bonded titles, but you've got to have a solid body of evidence or they're going to laugh you out of the courtroom:
301.192
Basically, it can NEVER have been titled or have a legit messed up title, not just a missing title.
Or....
You can go through the courts and basically sue the Missouri Dept of revenue to prove that you DON'T own the vehicle. I have a friend that's done this on several motorcycle titles. If you buy one and the title is in someone else's name, your money is gone and you have zero recourse.
And to be clear, Missouri has four title types. Regular green titles are just that, good to go. Prior salvage is branded as such and means "rebuilt", so forget about ever getting full coverage insurance. Salvage title means it CAN be rebuilt but isn't legal for road use as-is, and you have to have it inspected by Missouri Highway Patrol before they will sign off on it.
"Junk" titles are branded, and there's NOTHING you can do with that VIN ever again except sell the vehicle for parts. No state in the Union will help you and there's nothing you can do. Once it's in NMVTIS as junk, it's marked for life.