Yeah. It was a nice idea.
I've done some research, and found out the location of the .ini file in question. It is "/home/user/.profiled/custom.ini". (My ringtone is "Stargate Atlantis Outro.mp3", and there was no other file containing the text "Stargate". Without the quotation marks, of course.)
I re-wrote the value in the config file but the ringtone didn't change. Then, I rebooted the device and it finally changed.
Obviously, the device only reads the setting when it starts. (And also, I think the Settings application restarts the process responsible for it, however, I didn't try to find out which process it is. I think it would probably mess up with the phone functionality if the daemon restated that process while receiving a call.)

Later I found out that actually the device converts the selected ringtone to a mono .wav file. (And it also does that quite buggyly. )
Look at "/home/user/.local/share/sounds".

So, a work-around would be the followig:
The same daemon described in my above post, but instead of manipulating the config, it should also convert the personal ringtones to .wav, and then simply rename the files before the phone application plays them.