No, it's really not possible anymore. Even if you upgrade the firmware as far as possible, which I've done, you still can't log into the Kindle store on the dev

No, it's really not possible anymore. Even if you upgrade the firmware as far as possible, which I've done, you still can't log into the Kindle store on the device. For a while there was a trick you could do involving requesting a one-time password, but even that just doesn't work anymore, even on devices newer than mine. They stopped supporting the device, end of story.