I'm going on memory here, from about seven years back. I had a transmission rebuilt for a 1984 Z28, and they gave me two different springs (I think they were even different color). If I remember right, these springs were part of the downshift, one spring being more sensitive than the other. It could be you have a really sensitive spring in there that downshifts with only a little bit of input on the gas pedal and changing to a different spring would make it less sensitive. The springs were fairly small and made of a rather light gauge metal - they didn't look like anything I'd would have thought belonged in a transmission, in other words. If you have a transmission rebuilding shop in town, check with them. They usually have at least on guy on staff that can answer any question you can think of.
Good Luck!
Todd