Well soundly is relative. All of your assertions are also relative. How about some facts.
FACT In a 1/4 mile race the LT1 can expect to be beat by 0.8-1.0 seconds or about 10 car lengths. Best stock LT1 times are around 14.0, most in high 14's. Best WRX time is 12.8 with many low 13's.
FACT WRX STI is rated 0-60 at 4.9, LT1 camaro is rated
6.3. Camaro is destroyed off the line. (There's another relative term.)
FACT Power to weight ratio favors Subaru:
WRX STI: 3000 lbs. / 300 hP = 10 lbs. per horsepower.
LT1 Camaro: 3400 lbs. / 275 hP = 12.4 lbs. per horsepower.
Your camaro needs a boost of 70-100 horsepower (more than a few bolt-ons). A very good tranny as stated and a good torque converter, suspension/tire mods to allow full throttle takeoffs. Cheapest way is to spray it with a 100 shot, that would be a good race for 1/4. Of course you need more if the STI is modified.
Sorry to be the bearer of bad news. Hopefully that's better than finding out other ways.