Well, the news keeps on getting better here. Now I have my printer working.
I solved my problem by printing to my local USB port, rather than a network port. I thought that it was necessary to use port IP_192.168.0.1. In desperation, I just selected a local port (USB001), because the Shareport program said that the USB was connected, so I decided that it should be a local port in this case, and not a network port. And so it worked.
Just to recap - I am connected to the USB port on the DIR-825, and NOT a local USB port on my computer. I guess I must have missed the port to use (in the documentation) when connecting to the router through the Shareport software (virtual?) connection.
If I leave the Shareport disconnected from my computer, but have the Auto Connect enabled, then I get a message that the printer is not ready, but then the printer starts up (after Shareport has made the temporary connection, I guess). After the test page finished printing correctly, again the printer said that the printer was not ready. However, the print job was finished printing by then. If I just connect permanently (through the connect button on the Shareport software), then the printer just starts printing normally, just as it would if connected to a local USB port. So, I would say that it is working normally.
Perhaps I'll still see the other problems reported here about what happens after turning the computer on again after it has been off all night. But that is for another day, and I know how to get it going, at least!
So, it all works!
Al