The pipe is marked "22mm", and indeed is 7/8" in diameter.
I need a 12" - 16" seatpost to replace it. (note that there's a max of 7" seatpost inside)
However, unlike most "pipe style" seatposts, the 7/8" ones don't flare in at the very top... they're straight the whole way through. I could actually buy a 1/2" steel natural gas pipe (1/2" ID, 7/8" OD), and just use that!