Many things have changed and been re-designed over the years in the 4t60, so I do not think a 97 pcm will work.
This is a little more complecated than it might seem... but not impossible.
I know that the L36 and L27 harnesses are almost the same, so you may want to just keep your pcm and harness in the car and use that. Especially since you know your pcm will control your current trans. The L36 has 2 knock sensors instead of one like you L27 so, just connect the rear bank sensor and leave the front screwed in. There also might be some difference in length/connectors so you might need to do some cutting and soldering.
Also, my custom chip is based off an L27 program, so you could contact www.gmtuners.com
and get a L36 program burned on your chip for a little over $40.
And make sure you keep that torque-axis mount on the 97 L36 since thats the mount you'll use. ]
Another thing that I'm not sure about is if the rear manifold will bolt up to the DP. It might but I'm thinking it probably won't.
Thats all I can think of right now. It'* a shame your not a 94, that OBD1 pcm supported the 4t60/L36 bonnie in 95.(I think the trannys were the same in 94-95 too).