The rice approach is advised against in this forum (see some recommendations here).
Anyway, with the modular build of your FP2, you don’t need to send in the phone and can buy and replace your display module yourself:
On your FP2, this doesn’t even require any tools – other than your hands. 
If your FP2 has a two-part Slim Case, this is how to open and remove the case (both parts!):