The tailpiece that came with the drain is too short (4-inches). I need at least 6-inch. Unfortunately, the original tailpiece didn't have a separate nut—it was somehow welded/manufactured as part of the pipe. So when I bought a new flanged tailpiece, I needed a nut to attach it to the drain. The tailpiece is 1-1/4 inch, outer diameter. The threads are 1-3/8 inch outer dimension. I bought a 1-1/4 inch slip nut hoping it would fit (it was advertised as 1-1/4 x 1-1/4), and it does fit the tailpiece, but unfortunately the thread diameter is much too wide to attach onto the drain threads (inner diameter of the slip nut threads is 1-1/2 inch). I've been researching a lot and haven't found anything that appears to be what I need. Is there any nut that seems to fit 1-1/4 inch pipe but has 1-3/8 inch threads? I also can't find any tailpieces that are similar to mine but longer.
You need a tailpiece extension.
Reattach the original tailpiece that came with the drain and fit an extension onto that. Extensions are available in metals or plastic and can be trimmed as needed, etc. but, unless you like clogged plumbing, don't buy the flexible "accordion-style" ones.
Installed, it looks something like this: (Note: This is some kind of "before-and-after" picture.) What we're talking about is the portion in the center that shows the extension between the trap and the original tailpiece (chrome).