Problems with 95 Firebird Formula
 

My 1995 Firebird Formula (5.7 LT1) has a problem. It is in good condition and has only covered 98k kliks (according to the odometer). I have owned it for about 2 months and never pushed it hard enough to find the issue on the test drive.
When under hard acceleration and after it drops the initial cog it races away, but the engine stumbles and coughs before it will change up and it is like this throughout the gear range. But it only does this when under hard acceleration, under normal driving there is no problem.
I tried an after market software programer to see if it would resolve this, but only used the stock program.
At this stage I have no idea if this is an engine management problem or a transmission problem. I can sometimes here the transmission whine but it is not pronounced.
Any knowledge or advice on this would be appreciated.