Why not try EB1B?

Your LG can ask his boss to change his position from postdoc to something like research scientist, researcher, or research engineer, you name it. It looks like a permanent job even it is not. Then ask you LG to prepare a draft of employment letter stating that his job is in a research track. you don't need to mention the funding sources. The signature from the Dean of his school is enough.I believe his boss can help him because he's been staying with him more than 5 years.

Good luck!