Speedo affecting idle
I'll make an assumption that you have an LS1 with an LS1b ecm. You have a throttle cracker table for both P/N and in Gear. Is your ECM recieving a signal that your trans is in PN or inGear to tell it what table to use? I propose that when you start moving, the cacker table adds airflow and settles your idle. but when you stop that added airflow decays out and surging starts again.
So to keep it short, yes I think a retune would help this situation.

