The recently introduced Project Creator for JIRA plugin specifically addresses your use case (and thus JRA-720) and is looking very promising all around (haven't tried it myself yet though).
I'll also mention that the AtlasCamp 2013 agenda features a JIRA Project Templates topic, which indicates that realted functionality is going to be included in JIRA 6:
JIRA 6.0 brings a new Create Project experience to the table, making it easy for administrators to get started with JIRA for their use case. In this talk the Project Templates Feature Lead will explain what Project Templates are about, why we built them, how you can build a project template, a behind the curtains look at how it is built, and where we are going with Project Templates in JIRA 6.1 and beyond.
How both are going to compare remains to be seen, also the last sentence in the abstract seems to hint on this new feature not necessarily being as all encompassing as one might hope right away, but it sure looks like this pain point is going to be addressed soon one way or another.