As you well know Paul, I don't have a Git-Jenkins setup (yet), but off the top of my head, if I was concerned about the network latency and space consumption of cloning a full git repo across the network for every Jenkins job execution, I would approach my setup as follows:
(1) First, on the Jenkins build server, setup a single bare repo mirror of the remote repo. There are a number of ways to mirror a git repo such as executing a 'git remote fetch --all' on the mirror side or adding a post-commit hook on the remote side to push all commits to the mirror as they come in, so just google git repo mirroring and pick a method that works best for you.
(2) For your Jenkins workspace clone operation one or more of the git clone operations that gives the fastest clone and is suitable for a Jenkins workspace clone (see --local, --shared, --reference, --no-checkout, --single-branch and --depth options), some of which will give you a minimal, hard-link-no-copy or a shallow single-branch clone that might be useful only to use as a short-lived skeleton repo useful only for a for a Jenkins build of a single commit snapshot of a working copy.