The LS6 is great for most off the shelf cams. The FAST will give you the best gains with a larger cam, as in a 238/242 at 113 with .620 .6xx lift...
That's just an example, by no means is it what I would recommend.
You just want it faster than the gp? I would say a 23x/23x at 112-114 LSA and .6xx .6xx would be perfect. My old Z28 ran 11.6 with just the 228 r cam and 241 stock heads milled .042".
The guy that bought it from me sprayed that setup with a 175 shot and ran 10.6 @126 with a strong head wind with a DA of 3500 ft.
Get a built 4l60e, with the Ls1 you won't make tons of torque to warrant the 4l80e. I would recommend FTL or another known transmission shop. Get ahold of Greg at FTI for your converter, and personally I would swap to an 8.8" at least, the 10bolt is OK, but why not do it and not worry about it.
And I'm really not an Ls expert, I learn more about them all the time, but I have worked on quite a few, I give my advice based on experience and not off of the forums, lots of misinformation floating around.
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