I’m not familiar with Corectrl, but in Lutris if you configure your applications you can enable advanced settings and set advanced options like Command Prefix, or Pre-Launch Script, things like that.
The question is how does Corectrl apply a profile? If you can with a command… then see my previous sentence.
//EDIT: found this How to use CoreCtrl? - #4 by bill_t
Maybe explain how you set up everything on your side it will probably help.