I just took a look and it seems like 'bfa_ata4' is the only database row in wp_options specifically for bfa settings. I also noticed that functions.php references 'bfa_ata4' multiple times.
Is the functions.php the only place that this would be referenced or is it in multiple files?
so, in theory:
1. export atahualpa settings
2. change wordpress theme to something else (temporarily)
3. change wp_options options_name from bfa_ata4 to bfa_ata_whatever4
4. change atahualpa folder name to atahualpa_whatever
5. install new atahualpa theme
6. enjoy using atahualpa twice
does this sound about right?