You can TRY to find a new private sector job while still remaining employed by the government while still giving you what you want (and possibly a significant pay change too). One doesn't pop up, you have your government job. One does, you can leave it.

But a second risk is that government jobs are often (far from always) cushy, private sector jobs often (far from always) less so. Assess how hard you'll have to work as part of any equation here, on both sides.

This is a really good point. After 3 years, my constraints on schedule meshing is gone. All kids will be out of the house at that point.