[Accelo]

I had a similar issue and could not keep a reliable idle. I am using the exact same LS1 as you have installed. I have a BTR Stage II truck cam with a LS6 intake and headers. It was unsettling as any time I stopped I was not sure if the motor was going to die or not. As the idle is controlled by the computer using the idle bypass I wondered why the system would not control the idle better. Even with out the computer input that told the ECM the air conditioning was engaged. After getting the motor tuned all my issues with idle dissipated. The tune was $550. At the time I thought is as an expensive but not really necessary addition. I was wrong, if you have changed the camshaft a tune is mandatory in my humble opinion. AFTER the tune I had 354hp at the rear wheels. I didn't get a BEFORE reading as the AF was so far off the tuner thought one could possible do engine damage.
If you have a non-factory cam and a factory stall converter it can also affect the chances of getting a solid idle with the air on.
There are several well written articles on this very issue "Air Conditioning inputs to the ECM. Seems it changes depending the the year and model of the transplant. I was able to get mine to work. Wish you the same.
Cheers