Excellent illustration Paul!

I think you have it spot on. Another method I would try to break them loose is to take a rubber band, cut it with scissors, secure the bridge base in a vise and put the rubber band in the slot and applying pressure see if you can it them to move.
If that doesn't work then I'm guessing that they are rusted and may need some light sanding on the mating surfaces. You can disassemble these in the same manner that they were made. Basically these little pulleys were turned from a round piece of stock that had a hole in the center. The center hole is the same size on all six of the pulleys. Once they parted these little pulleys on a lathe they would have sanded both sides to take off any burr left behind in the parting operation.
The saddles I believe are all the same height and they also have the same size hole drilled through. To make the assembly they had to take a small piece of wire and push it through the saddle, with the pulley in place, to the other side and then file the ends flat. This created the tiny axle that the pulley spins freely on. Eddy Elliott, a forum member, used to make these bridges when he worked for Mosrite.
To disassemble you need to reverse the process. The most difficult part is going to be finding something with a smaller diameter than the axle and yet strong enough to push through the saddle. If you can do that, you will be able to remove the saddle and clean the mating surfaces and then reassemble.
I do not think that these are a "pressed fit" in machinist terms. The first method I would try would be the following:
1. Remove one of the saddles from the bridge
2. If you have a vise I would close the gap so it is small enough to allow the saddle to lay on top with enough room for the axle to push down without hitting anything and getting bent.
3. Take a standard pin, such as used in sewing cloth, and cut it with wire cutters to about 1/2" long. If there is a burr left from cutting it, sand that off. The pin will be pretty strong and have a head that you can push on.
4. Hold the pin with a pair of needle nosed pliers and center it on the axle. With your free hand place something flat on top of the pin head and apply pressure to see if you can get the axle to move. If it were me, I would use a butter knife because it's nice and flat and you can rest your thumb on it without getting hurt.
5. If the axle moves I would push it through until you can remove the pulley. I don't think I would push it all the way out though.
6. Once the pulley is free I would use a very fine grit wet/dry sand paper on all of the surfaces, such as 600 or 1000 grit.
On the first attempt, if it does not work, I would try from the opposite direction, just in case. If it does work, be very careful not to lose any of these tiny pieces. I have seen bridge for sale on eBay with missing pulleys and you can't buy these at the hardware store.
If you are not able to exert enough pressure to push the axle through AND you haven't bent your pin, then you could use a small drill press as an arbor press and push it through that way.
If the pin isn't strong enough then it's going to be tough to find something with a diameter that small that is stronger. One thing that comes to mind is a small nail set that could be ground down to a smaller diameter.
Jeez, I wish I had one of these bridges in my possession I would give it a go.