For Southern Tier, I think the Lynskey would work great. I have no clue how yours is configured, but I am assuming you set it up with the kinds of parts that you would want for long days in the saddle. My Lynskey Backroad is probably a similar frame to yours, but mine I think has more metal and larger diameter tubing in a few places because they designed mine to take a heavier load. Some photos of mine at this post:
Touring on titanium frame?

Motobecane, I have no knowlege of it and I do not know their line of models. So, no opinion.

My folder has 24 inch wheels, Airnimal Joey. For Big Bend, it had the advantage of being able to take it on the plane for free (Southwest Air, two free checked bags that are 62 or less inches). And that was a week long trip, if I decided that it was the wrong bike for the trip, it was only a week so no big loss. I had owned that bike for over a decade but had not really ridden it very much so part of my bringing it was curiosity. And also I was considering taking it on a trip on Amtrak and folding bikes can be taken on Amtrak as a carry on, so the Big Bend was an opportunity to ride that bike for several hundred miles to see what I thought of it. More on my folder here:
Folders in the wild - post your photos

Southern Tier, I think the priority is what bike would you be happiest riding for a couple of months, packability is much less of an issue. If I had a Bike Friday, I would leave it home and take a 700c bike. As I noted in my other post, I would either bring my Lynskey or my rando bike, they both would work well for long days followed by more long days. I built up both of them from parts, so I know how they are put together in the event one needs some work on a long trip.

I have zero experience with tubeless tires. But since mountain bikers use them where there are lots of thorns, maybe the tubeless tires would work well in the southwest where one of my friends had lots of flats when he rode Southern Tier.

On your Lynskey, if you have replaceable dropouts in the back, note my comments on locktite at this post:
Lynskey Backroad Build

You really do not want those little 4mm screws to loosen up from vibration. I use the term locktite as a generic term for threadlockers, other brands work well too. I have used different brands over the years, this is what I bought last time.
https://www.truevalue.com/6-ml-remov...hread-locker-1