reducing object store size with remote alternates or shallow clone?

I'm trying to package a linux kernel source tree and would like to just tar up a tree with .git/.  However this is a bit problematic as the size of tgz is about 500M which exceeds the limit of the image I'm trying to produce.

I was wondering if anyone had a means to reduce the size drastically.  I'm ok if a post processing step is required to get full git support.  One idea I had was doing a shallow clone and if there was some means to "reconnect" it to a full work state after the fact.

thanks

- k