If you don't care about the cups, and they are soft metal (you said anodized so I guess they're aluminum), why not just lightly file them down to near JIS? Forcing aluminum cups into a steel frame would also work, but be careful you don't deform the cup. The frame wins that fight because the aluminum is really soft metal compared to the steel frame, and we know the cups are pretty thin walled because they fit between the steerer and the headtube. Done properly, you'd probably just have a JIS headset at the end of the day.
It's not much you need to take off. Concentricity won't matter for such a small amount. Headsets are designed to take a bit of off-center if necessary.
If you want to get into reaming, you could do what I did. I just made a reamer out of a shell-reamer and some threaded rod. I took a reamer that was sold on ebay as 6-thou undersized 1-3/16". Turns out it was worn and cut too big a hole, luckily I tested it on some scrap. I took a sharpening stone to it and took it down to 30.1mm. That's about perfect.
Used a lathe as a guide to do the actual reaming. Of course you wouldn't have a lathe (but hey, a lathe is cheaper than buying the park tool). But I manually turned the lathe so I wouldn't get into trouble.
You could get a shell reamer and a piece of threaded rod to fit it, stone it down to size, and just not worry very much about centering because you're taking off so little. Run the threaded rod down the headtube and build it up with tape so that it centers. Give it a nice crank. If you can drill a hole in metal without breaking the drill bit, you can do this.
Alternatively, you could get one of those adjustable reamers. They can be had used on ebay for like $30. You'd get the size that goes up to 1-3/16, and set it a hair under. Wrap the nose of it in tape as a guide. Because you're near the max size, the blades will be set back and you'll have a nice threaded nose on the reamer to wrap tape around and pilot with. Remember, it's adjustable, you can use that to your advantage. Set it just a hair over what you've got and take light cuts. Go gradually up in size, taking light cuts, until you get your desired diameter.
This can be done, cheaply, by the amateur home-gamer. Lots of people will say it's stupid and you'll ruin your frame, and I do recommend trying it out on some scrap to get your feet wet first, but this isn't rocket surgery.
The trouble with the brake cylinder hones is not that they're going to take you off-center. Not for this little of a change in diameter. The problem I'd foresee is that the original reaming is probably not very deep, and often those hones have stones that are pretty long. If they overlap the step in diameter between the JIS-reamed section and the rest of the unreamed tube, they won't be taking off metal for the whole depth of the original reaming. You'll end up with a taper. Of course, if the tube started out JIS size and isn't reamed at all, then a hone could work just fine.
Edit: Ah, but I see
son_of_clyde recommended a ball-hone. This could work too. Lots of ways to skin this cat!