Hi,
Finishes that have the same thinner such as mineral spirits usually are compatible. Turpentine and mineral spirits are compatible as well. I would lightly scuff the surface with a maroon Scotch Bright pad or 320 sand paper and then put on the polymerized tung oil. Use the tung oil the same way as the T&T. Put it on thin, let sit for 15 minutes, and then wipe off all excess finish. even in every corner. Then let dry 24 hours before the next coat no matter how dry it feels. In warm (>65 degrees F) and dry conditions S-W polymerized tung oil will feel dry to the touch in as little as 3-4 hours. If put out in the sun on a warm day, it will feel dry in 2 hours. Don't add another coat. Wait 24 hours no matter how dry it feels. From the standpoint of weather resistance, the polymerized tung oil is better than linseed oil based finishes but can have exactly the same look and feel. That is why I've used S-W polymerized tung oil for over 30 years because I can use it to recreate almost any authentic looking finish. Inevitably someone will write that tung oil takes forever to dry and may never cure. They are confusing raw tung oil with polymerized tung oil. The polymerized oil is heat treated and mixed with solvents so it dries very fast. For example, you know how long it takes raw linseed oil to dry, right? Well Tru-Oil, which many of you use is simply polymerized linseed oil. It dries pretty fast, right? Anyway, Sparrish, you should not have any problem using the S-W finish on top of T&T. The important thing is to keep your shop warm and above 65 degrees because any finish risks clouding if applied when the temp is much below that, particularly if conditions are humid. The other key is to be fanatical about wiping off the excess oil.
dave