There's pretty much no way around it, just exhaust physics at work.
You're allowing upwards of 50% more flow to a resonator and muffler not designed for that much exhaust. If you read up on how gasses like to flow, bent tubes vs. mandrel bent tubes, and really any custom exhaust forums you'll get a good idea on how unhappy exhaust can get(raspy).
I designed a custom exhaust for some Volkswagen R32's (THE raspiest engine on the planet) and it takes a lot of fiddling and matching to lower the rasp.
But no worries, I've got Berk HFC's on my stock Z exhaust and it's raspy. just the nature of the game.
The only way around it is to get an aftermarket catback setup (not NISMO), or just larger exhaust tubes.