That is a nice car. Sadly T-tops are the weakest of G bodies and more prone to twisting with high HP. Even a hardtop needs reinforcing above 400 HP. My 305 is making 250 HP, not the quickest car but no dog either, but enough to cause some cracks
![Frown :( :(](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
. But if it is greatly out of tune or a LG4 then it would be a dog. I hopped mine up 6 years ago when there were alot more direct fit performance parts available for these cars than now. I highly suggest start with replacing the body mount bushings, and don't be surprised if the frame mounts may need some repair washers welded in. Weld in a rear seat brace, and weld on or bolt on rear LCA mount braces. Build a rear frame brace, and install a aftermarket front frame brace. But with the more quickly rising stresss of a turbo motor you would be better off using a hardtop and leaving the T-top alone or not above 400 HP and leave it N/A is my suggestion.
In stock form, a CCC engine has 2 idle speeds, fast idle when the engine is still cold which is 2K RPMs, and curb idle once the engine is warmed up which is 650 RPM. Sounds like it is not kicking down from fast to low and probably a choke problem as already suggested. Since T-tops are more prone to leaking, be sure to keep it in a garage when not in use, just in case. The throttle shaft bushings in the Qjet carb are well known to wear out and leak vacuum by 100K, as well as the timing chain needing replacement by then. Stock timing chain are not too good.
Years ago, there were alot of direct fit performance parts available such as direct fit and fully legal TES headers and Crane Powermax cams. Here is a link on how to build up a L69, but it is dated since many of the listed items are no longer made but can still be found used.
http://www.montecarloss.com/SSThunder/ELengines.html