Usually servicing a transmission after its not working right makes it worse. I would start looking into a 4l80e with the HD2 kit if you plan on upgrading power later on. I rebuilt my transmission in my shop class when my 3-4 clutch pack went and beefed everything up. I only had 65,000 miles. The weak point on the 60e's is the whole transmission basically. 4l80 is the way to go.
2002 ECSB 2WD 5.3
1995 Formula Firebird 383 LT1
1984 Camaro 408 SBC
Most sports require one ball, motocross requires two.
Racing isn't a matter of life and death, it's much more important than that.