I feel for you, and I hope this works out for you in the end. I'm in the private sector, and have been actively searching and applying for a year, and I've spoken to two recruiters. I'm pretty well qualified for the roles I've been applying to, but it's a fairly niche skill set so it's been maybe 70-80 applications over the course of the past year.
I've never been happier to have been out of the government; I left a few years ago.