1-7/8 vs 2" is super marginal difference, even on an FI car. I'm betting less than 10hp and probably only at peak. Up to you where your $/hp is worth it.
Some info here, but I think it is a bit outdated.
https://www.camaro6.com/forums/showthread.php?t=472259
Pray always recommends 2", even on N/A cars.
As for rasp, yes, headers+npp+no cats is raspy AF at 50%+ throttle. Not too bad at lower throttle though. I personally like it, but it isn't for everyone. Also, sounds fine with the npp closed.
I would NOT run cats on an FI setup with cheap TSP cats. Pay the money to get kooks green or go none at all.