To Darren:
I was afraid that it was impossible to modify the LV-Simulink connections, so that's why I was trying to use another set of controls in between (see my first post picture), which would allow me to keep the same connections during the execution.
To Paul:
I wasn't aware of the "value (signaling)" property... I've tryied it, and it works just fine, so I just have to get my cases right in my program to have it working correctly!
I don't know if it will be useful, but I'm posting the VI I used to test this.
Thanks for your help!