Ok, so it wasn't the use of CLDC 1.1 that caused problems when trying to run Dweller on Nokia handsets. I do however think I've found the cause now, and it has to do with signing of the Dweller.jar file. I had always thought that signing a jar file for deployment on a phone worked the same way as when signing a normal jar file, but I was wrong.
I have decided to ditch signing of the J2ME version of Dweller. The primary purpose of signing a J2ME jar is to not have to ask for permission from the user to access certain parts of the API. And I'm not using any of that in Dweller so it's safe to publish Dweller as an unsigned jar.
I have uploaded a new version of Dweller for J2ME (1.16.9). I would very much appreciate if any Dweller players using J2ME handsets would report back to me if the latest version is working or not.