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You can push the torque converter back only about 1/8 of an inch without removing the transmission. You wouldn't be able to access the flexplate bolts with a wrench and definitely wouldn't be able to remove the bolts. The tranny needs to be pushed back about 3" at least. I use a Hays SFI approved flexplate.
Removal, Haven't done it on the Vette but did on an Impala. Get 4 grade 8 bolts 3/8 X 16 4 inches long. Remove drive shaft. With the trans supported remove all 6 bell housing bolts. Replace two lower and two middle bolts with 4 inchers. With TC loosened slide the trans back 3 inches. Keep it supported. R&R flex plate, slide trans forward bolt up. Might sound complicated but the method does work. I have done two like this, last one took something like 4 hours.