Does anybody know if the 62 grain TTSX will stabilize out of a 1 in 9 twist?

It should. The 70gr won’t though.

That chart is for normal lead bullets though. Monolithic copper bullets are not the same. For example, the 55 grain TTSX requires a 1 in 9 twist. Notice I'm talking about the Tipped versions of the TSX not the normal TSX. The tipped version is longer.

Worked fine in my 1/9.  I think it all depends on the barrel.

<This. Not all barrels are exactly as marked. Depending on the manufacturer, twist rates can be +/- a little.

Many 1:9 barrels can shoot and stabilize 75/77 grain bullets, even though they are borderline not supposed to. Some 1:9's simply won't shoot them well.

All copper bullets, Barnes, GMX, etc. are considerably longer than their weight would indicate. Comparing them to a 62 grain M855 is probably not going to match up exactly. The bottom line is you are going to have to try them in your rifle to find out. I believe Barnes has twist rate suggestions included in their online reloading data base. I would check their first, before committing to a large purchase, after all, Barnes bullets are not real cheap.

Barnes lists 1:9 twist (or faster) as being needed for use with their 62 grain Tipped TSX .224" bullets.

The 62gr TTSX is a hair longer than the 69gr SMK ....

Bullet lengths, ballistic coefficients, etc for many many bullets listed here, with a great filtering feature - https://www.xxl-reloading.com/Bullets/