Stock 4L80E with a TransGo HD-2 shift kit upgrade has been used for many years on cars making under 1000hp. That trans will probably suck up a few HP due to parasitic drag.... but you won't need to worry about giving it a nice thrashing.
They make Tbrakes for them also. Jake's is a respected builder.... as is Rossler, Mike's transmissions, etc.
Just do some google searching.
http://ls1tech.com/forums/automatic-...uch-power.html
The stock 4L80E torque convertor is a monster and weighs a ton. There are a number of aftermarket ones out.... for your power level you are barely tickling the power levels this trans can handle. The internals of a 200-4R look like twigs compared to the 4L80E big brother.
To do a T56 swap as said does cost $5K without blinking an eye in parts once you factor in the trans (T56 Magnum), good clutch/fly, slave, bellhousing, etc.
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Project: 1969 Chevelle, alum 5.3, GTS76 turbo, Chiseled Perf A/W intercooler, Holley Dominator EFI, Davis TC, JRi coilovers, 14" brakes, T56 Magnum. CTS-V Recaro seats!
Coffey Fabrication Nashville, TN doing the fabwork! 800rwhp+/25mpg+/9's@150mph goal
https://lateral-g.net/forums/showthread.php4?t=52976
1993 Mazda FD RX-7, built LS7, T56 Magnum, Holley HP, Davis Tech TC, 8.8" 3.73 Cobra IRS diff, DSS axles, Ohlins coilovers, big brakes.
CCW 18x11 front 315/30/18's and 18x12.5 rear on 335/30/18 RA1's,
2850lbs
10.31@137mph 165mph Shift-Sector 1/2 mile speed
441ci AllPro headed motor and 200lb weigh reduction in the works....