I've had a rummage on the internet, and all the Texans I can see (12s aa well as 6s) have a very unusual bridge. It doesn't have pegs like a usual modern flattop, and it isn't a tailpiece like many archtops.
It's a thread-through bridge, so you thread the strings through a part of the bridge assembly (roughly parallel to the top and still outside the front of it) then wiggle them round a saddle that is height adjustable with a knurled nut at each end.
Now I've had a Framus 12 like that to pieces (it's at a friend's house at the moment, so I can't check whether it's a Texan or not), and the whole bridge assembly is BOLT-ON. I think the securing bolts are underneath the adjustable saddle, and there are some more nuts inside each of the little metal caps at the end ofthe moustache of the bridge.
The one I had to pieces was also sharp up the neck. I'd already had huge fun getting a spanner with slim enough jaws to do the trussrod (7 mm I think) and eventually I had to enlarge the hole for the trussrod nut a bit, all covered when the cover went back on. When I got the bridge off, the holes the securing bolts went through were oval. Under tension, and perhaps previous fiddling, the whole bridge assembly had slid towards the nut. On mine the front was also badly bellied (previous user had put 13s on it, and IMHO 13s is too much for almost any 12-string front or neck) and I had to make a home made equivalent to a "bridge doctor" too, but it doesn't sound as if you have that problem.
So I marked the front with a fine felt-tip pen, extended the ovals of the holes backwards a bit (you could shim the holes if you are getting anal about it) left the strings off, assembled the bridge loosely, slid it back along the guitar until I could see it was about an eighth of an inch (a bit more on the bass side) back from where it had been, and then tightented the securing screws up to fart past grunt. Strung it. Watched to make sure the assembly did not sidle forward again. Bingo! Near as bollox is to swearing!
I've left the felt-tip marks on so I can see if it does it again. If it did, a bit of not-too-secure glue and 24 hours before re-stringing ought to sort it. If you use the right felt-tip, you will be able to polish the mark off again.
On mine someone had also deepened the slots in the bridge (no doubt to try to lower the action to make it playable despite the bellying) to the extent that the strings were "ringing" on part of the steel bridge assembly. That I dealt with by a real bodge - cut a section of wire from a wire coathanger, put a bit of glue on it and held it the tail side of the saddle while I brought the strings back up to pitch. It pinched in tight behind the saddle, so also effectively moving the saddle back a bit, and the existing slots in the saddle then were just far enough out of the way not to buzz. The thread-through holes were accurate enough that the strings still lined up correctly.
It never had had any balls to the sound, very quiet for a 12, and it still hasn't. Tried 10s, really too light. Playing 11s now. Before it went to visit my friend some people were really rude about the sound ("I can't see why you play that thing", thanks Simon) but I thought it had a nice middl-ey jangley singing sound, easy to sing to, not so loud you had to yell to get over it, and by then it was playing really easy and mostly staying in tune, unlike many 12s over an evening. A local semi-pro said it sounded "delightful" but I think that's going too far!
Not a patch on the Hagstrom 12 I am playing now, not as loud as Simon's Yamaha 12, and nowhere near as loud as Slats' Washburn 12, but vaguely all right.
Incidentally, quite a number of Framuses on ebay right now, mostly the 12s.
But there are Texans including 6s at various prices on the internet in various places at various prices, and if you really do like the sound, you may want to let your fingers do the walking.