Record the effects vocal technique with a dynamic mic and EQ out a lot of the low end to reduce the popping. Have the singer do the take again but singing it or performing it normally with a condenser mic and pop filter and mix the two signals.

Okay, that sounds good, but another problem I have is that this is screaming vocals so I'm afraid that a condensor microphone wouldn't be able to handle the SPLs.

What rain is saying is not only do two recordings do it with different mics. Let him hold say an sm58 with his hands screaming then do another take with him singing like he normally would, even if he never sings during that part. When he does the singing let him use the condenser mic, then yelling use the dynamic, if you don't have one get one they are a must, I personally use a sm57 but a sm58 will do the trick the same.