With a chuck, the lathe works fine for turning the pipe. My problem is really finding the right cutting tool and technique for holding and moving it. That's where the router and jig come in. You do raise good points, though. Maybe I need to consider other options before getting too fixated on the idea of a router and a jig.
I think a metal lathe might be more suited to the type of thing I'm trying to do, but I don't want to buy another lathe right now. It could be that I just need to work on my technique, once I've identified a good cutting tool.
I do have a dremel tool, and I've been experimenting with various bits - cutting the pipe while it's turning in the lathe. With the right bit, the dremel tool followed by a file produce acceptable results, but I'm sure the process can be improved.
I've also tried a small sand paper block (60 grit) and a wood chisel. The sandpaper clogs and doesn't cut very fast. The wood chisel is more difficult to control and can gouge the pipe if I'm not very careful. My disc/belt sander goes through the pipe like butter. It's very good for putting a square edge on the end of the pipe, but not so good for the degree of precision I'm trying to achieve with my tenons/nipples.