TWDB dates the serial number to 1960.

You may have to adjust the carriage height, but in doing so, you're going down a realignment rabbit hole. The problem with adjusting the height of the carriage, is that you're adjusting the strike point in the typebar travel. Carriage adjustment on the TP-1 is nearly perpendicular to the segment, so you would not really be changing much. If you loosen those screws, you need to make precise witness marks before doing so, in order for you to return the machine to its current state if you get lost or the adjustment doesn't do what you want.
Have you had your platen re-covered? My platen had shrunk significantly since 1959, when this machine was produced. It was as hard as 1020 bar stock and also almost 1mm narrower in diameter. This is a big deal with a machine as precise as the TP-1.

Phil Forrest

dragon typer wrote:

Thanks for the cautions, Phil.  They are well-taken.  Do you happen to know where the vertical adjustment screw/s for the carriage are located?

See this link: =13pxhttp://gallery.leica-users.org/d/526413-2/P1000561.JPG
The adjustment screws are in the center of the photo. This is the left side of the typewriter (carriage/line space lever side). The right side of the carriage has a corresponding set of screws.
The screws which set and hold the carriage rail are the pan head ones sitting in a shallow oval depression in the carriage rail. They are on either side of the main adjustment cam/screw which is sitting in a larger oval hole in the carriage rail. Both left and right sides of the typewriter have these screws for adjustment. From here on out, I'm backing away from this one because messing up that alignment is one of those things that a tech is going to be really happy and upset that you have done, if you have to send it out.
Happy because it's going to make that tech much more money. 
Upset because it is not something that anyone should really be messing with and there is going to be frustration and profanity involved in getting it perfect. 
I'm recommending against it, is all.
If you can't get it right, feel free to contact me if you want to sell it.

dragon typer wrote:

As for platen recovering: I was waiting to see if I could align it before putting the $ into recovering the platen!  Are you suggesting that recovering it and adding more thickness (even 1 mm) might resolve the alignment problem?

Yes. The less circumference your letters have to strike is going to affect alignment.
Are you body bushings (and the metal bushing supports) in good condition? Are the segment left and right bearing races completely free of dirt, grime, polymerized oil?
Has the shift lever assembly been bent at all, ever? 

Phil Forrest
 

When you replace the body/chassis rubber bushings, make sure you have the metal inserts which establish appropriate clearance. With these metal sleeves, you can fab up new rubber bushings using automotive vacuum hose and rubber o-rings. There is not really a source for these, though Peter Short said he could make them, but just one set would be cost prohibitive. If a few folks get together, we could have J.J. Short make the molds for the several sizes of rubber bushings for the TP-1 and save a little $$ by volume.

I was looking at the segment on my TP-1 and the linkage which actuates the escapement behind the segment comes really close to a chassis part when the shift key is depressed. Could this be part of what might be hanging up your segment? I haven't had the chance to have the bottom cover off of my machine to try to diagnose this issue, and I'm not sure when I'll get a chance.

Phil Forrest