In the process of fixing it properly, I realized that I was using quite a startling amount of stuff, so I thought I'd chronicle it for other people's amusement.
First, dealing with the cracks. They were relatively straight, so I used a small hacksaw (1) to cut the casting apart along the path of the cracks. I then used a surplus dental pick (2) to scrape off some "J.B. Weld" epoxy that was on some parts of the cracks where I'd previously tried to fix them. (The previous attempt didn't work so well because the cracked piece was still out of alignment, and the epoxy was old and didn't set up right.) I also used a half-round metal file (3) to remove some burrs and clean up some bits of the cut surfaces. So, at that point, I had the base in two pieces, which could sit in the appropriate relative positions to each other with a small (0.5 mm or so) space between them.
Second, the work surface on which to place the base parts to reassemble them. I had intended to use a piece of glass I'd salvaged from a scanner a while ago, but I couldn't find it easily, so I decided to disassemble the anti-electron-radiation CRT monitor shield (4) that came with a monitor I bought years ago and which I had utterly no use for -- but, for purposes of this, it is a nice piece of (conductive, I think) glass in a cheap plastic frame. To remove the glass from the frame, I cut some tabs off the frame with a small razor-saw blade (5) and pulled it apart. Then I cleaned the glass with Windex (6) and a paper towel (7).
I then took a piece of scratch paper (8) and sat the large part of the base on it, and traced around the circular outside of the base with a pencil (9), making an arc that I could use to align the pieces against. I then taped the paper to one side of the glass with Scotch tape (10), with the arc against the glass. After flipping the glass over, I then applied a piece of Saran wrap (11) to the glass -- thereby obtaining a very flat work surface that I didn't mind getting epoxy on, with the alignment arc visible through it.
Third, the means of reattaching the pieces. I couldn't find any new J.B. Weld at the hardware store, so I got some Devcon "Epoxy Steel" 90-minute two-part epoxy (12) that seems pretty similar. Epoxy by itself is pretty runny, though, and not all that strong in large lumps, and that 0.5 mm gap needs filling. Thus, once I had mixed up an appropriate dollop of the epoxy, I mixed in a good bit of bronzing powder (13), which is a very fine copper/zinc alloy powder used for either this purpose or applying to statuary to give it a metallic look. I mixed that in thoroughly, and the result was a bright coppery-colored thick goo, which in theory will set into a very strong metal-filled-epoxy composite material.
I cut a strip of plastic off of the plastic card that formerly held a T-Mobile SIM card (14) with an X-Acto knife (15), making a handy mixing stick and applicator for the epoxy. (Old credit cards and similar things are a great source of sturdy little bits of plastic.) Using that, I applied a thick layer of the epoxy/metal goo to the cut sides of one of the base pieces, and placed it against the other base piece, with both of them sitting on the glass sheet -- thereby ensuring that the bottom surface is indeed absolutely flat like it should be, and using the pencil-arc guideline to make sure their alignment in the other directions is reasonably accurate. Tomorrow, it should be all cured, and I'll use the file, the X-Acto knife, the dental pick, and possibly other tools to smooth off the excess epoxy, and it should be all fixed.
The thing which I am particularly please with is that, aside from the first glass sheet that I couldn't find, I had no trouble finding any of the things that I needed to do this. That's sort of a new thing for me; it's only fairly recently that I've been organized enough for that to happen.