Shawn, there are a lot of potential approaches here, but one I'd recommend is what DoD code.mil is doing. See:
https://github.com/deptofdefense/code.mil
The idea is basically this: A project will generally start out with public domain code in the US (to the extent it has been created by federal civil servants). But the project will designate a true open source license at the outset, such as GPLv3 or the Apache License 2.0 or what have you, and the project will use the Developer Certificate of Origin with the understanding that non-civil-servant contributors are agreeing to license in their contributions under the designated open source license. Over time the project becomes a mix of (a) federal civil servant code that is public domain in the US, (b) federal civil servant code that is under the designated project license outside the US, and (c) code from other contributors that is under the designated project license.
As further explanation, note that the statement that US government employees "cannot hold intellectual property" is not correct. What is true is that in the US Copyright Act, works by federal civil servants in the scope of employment are outside the scope of copyright - i.e., public domain. However, it is generally agreed that this has no applicability to works published outside the US. Software today is generally published simultaneously in multiple jurisdictions (for example, the SCAP Security Guide, by being published on GitHub, is published internationally in multiple countries).
I have a contact who is a lawyer for the code.mil people who may be able to help if there is interest in this approach.