RE: transmission trouble
A company called Gear Vendor makes an over-drive unit that will bolt onto a C6. An added support brace is needed. Then with maybe 3:70 ratio, you'd have basically a 6 sp automatic. You'd have the best of all worlds. Lots of off the line acceleration and be about 2000 rpm at 70 MPH. I believe the unit is around 1400 bucks. Works off a switch. They've been around for a long time. They've been making making OD units for Motor Homes for 20 + years.
This unit is aprox # 15 on my wish list, right after a 428 CJ cleverly disguised as a 352. ha ha . . .
1960 Convertible (Orig owner)
Pic of car with my son Justin (15 Y/O 6'1")
Poss 3rd Gen T/B owner