So when I said that the J-pole was soldered together, I neglected to mention that the coax - the thing that I connect my radio to - had not been connected to the antenna.
To begin with, I used a borrowed antenna analyzer (a MFJ-259) to find the point on the antenna where I got the lowest SWR. I then marked those points (there's a point on the 3/4 wave section, and a point on the 1/4 wave stub, and in theory they should be at equal height) on the antenna with a Sharpie. Then I screwed a chassis mount SO-239 connector (photo) into the 1/4 wave matching stub, and added some copper wire wrapped around the base of the connector. This was intended to improve the electrical connection between the 1/4 wave stub and the side of the connector that connects to the shield of the coax. I'm not sure it was strictly necessary, though. :)
I had previously soldered a piece of solid core copper wire that I had laying around to the center conductor of the SO-239. After I got the connector screwed into the 1/4 wave stub, I tried soldering the end of the wire to the 3/4 wave section of the antenna at the low SWR point I had previously marked. My soldering iron wouldn't get the copper pipe hot enough for the solder to stick - not surprising, since copper is an excellent conductor of heat - so I ended up using the blowtorch I had used to solder the antenna together to begin with. This worked much better, and when all was said and done, I had an SWR of between 1.1 and 1.2 at 146 MHz.
Today I covered the wire and everything but the threads on the SO-239 with electrical tape to protect them from the elements, and to make sure that nothing could short the matching stub and the 3/4 wave section (apart from the bottom of the "J"). I then (with my upstairs neighbor's permisssion) attached a couple of U-bolts to the railing of the back staircase. They will hold the mast that the j-pole is mounted on to the railing. I might fabricate another mast out of something or other later to get some additional height - I haven't decided yet. I didn't connect any feed line to it, as I don't have a UHF -> F adapter.
Soon, I will have a working outdoor antenna!