Answer: this is not allowed in the Android Market, because the Market does not allow downloading two applications with the same package name. Android cannot be tricked into installing a premium version of the free version and treating it as an update.
The good news: adding database backup and restore features (copying the database to the SD card and back to the application folder) required a few lines of code. My users will need to install both versions in parallel, back up the database from the free version and restore it to the premium version.
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