SpyderHunter, there are a few issues to deal with here. First the tunnel will need some attention for a 700R4, while the 4L60(E) is a direct blood cousin [or maybe sister] to the 700R4 I have only read about the 700R4 [so I can't add any definite absolutes]. All variations of the 700R4 are longer so they will almost certainly need drive shaft work [you might win on that one as yours has already been shortened and therefore you've already dealt with the torque arm length/mount issues. The 700R4 has a 3.06:1 first and a 0.76:1OD so your rear gears won't need to be as low as the 2004R with it's 2.74>2.86:1 first (the sites I have read seem to have a discrepancy on this number) and a much higher 0.64:1OD so this would mean the rear will need Zoomies to run at a decent enough RPM for the highway. with all of that said to make the 2004R live with any power you will need to spend
MONEY There is also the fact that the 2004R is not a direct bolt up to your LS of (any)choice there is a difference in crankshaft stick out Sorry I can't add more on that. The 700R4 is much more robust than even a decent built up 2004R especially by the time they went to theL6XX nomenclature, the one that is matted is already suited to that engine even with some decant upgrades. So in short for me the right tranny is going to be the 2004R, but for your engine and what your car sounds like to me is the tranny with that motor. there are down sides to both if I had decided on the LS6 [that I still want] I would have gone with the 4L6XX tranny. A little long winded I know but I hope I added some clearer insight into the matter. Harry Oh 4L6XX means: 4L60/65/70(E) And for your reading pleasure, the links on the left that may apply [or all of it]:
http://h-body.org/library/hbodyfaq/index.html and cross member movement will have to happen with any appropriate OD tranny. I also forgot to mention the speedo 2004R will likely need an adapter/right angle drive for the stock head unit, the 4L60(+) will likely need an expensive remedy like an electronic/or GPS speedo conversion or a CableX:
http://www.abbott-tach.com/cablex.htm
I'm not a hoarder I'm a preservationist 78 Monza Spyder (~Soon(ish +/- I guess) To Be 2+2 with Spoilers)