I had no success in attempts to downgrade. However I discovered a really weird workaround which allowed me to run Media Composer on the new macbook pro laptop with Mavericks.
I copied Media Composer from my OLD laptop to the NEW laptop using Migration Assistant and copying the applications folder. Then accidentally discovered I could successfully run media composer off of an external hard drive that was a clone of an existing 10.8.4 system.
So I decided to partition the hard drive on the NEW laptop. Partition 1 was OS X Mavericks PLUS the applications folder copied over using Migration Assistant (including Avid Media Composer). Partition 2 was a copy of the 10.8.4 clone I had in my possession which already had Avid Media Composer.
Launching Avid Media Composer off of Partition 2 works. I have no idea why, but I’m running with it at least until Avid says they support Mavericks. Hope this helps anyone else having similar issues.
Dan