That’s where the data is stored, so there is no alternative if you don’t want to lose all the stories. I guess you could try just saving the tables that contain the module data (xx_modules, xx_module_privacy, xx_module_settings).
Your census problem is not (can not) be related to the database, so you should backup your database, re-install kiwitrees, then import the backup of your data into the new database. At the very least you should try that before you spend a lot of time doing anything else.
I say “Your census problem is not (can not) be related to the database,” with confidence because at the point your census display fails there has been no reference made to the database. No data has been received from it, nor sent to it.