Cam changes aren't a great way to alter exhaust sound as it isn't easily predictable and can wind up with the wrong profiles for your driving style.
These guys make the best exhaust components I've seen - https://shop-solo-performance.com/en/24l-pontiac-solstice-years-2006-2009/1409-2006-2009-na-axle-back-exhaust-kit-pontiac-solstice-24l.html
That rear system, if it suits the budget, should solve the issue. $334, owner installable and reported to improve the sound - you could post for actual users here to see who knows first hand.
I have this axle back exhaust, I did it myself in the garage. I think it sounds great. It has a nice lil throaty sound and it was within my budget.