So I finally found a posting for an experienced position at NG that didn't require an active clearance. Now I think I know why NG doesn't sponsor experienced professionals for clearances: according to the NG recruiter, the process takes up to 11 months. I can't see many hiring managers willing to wait around for 11 months before their new employee shows up for their first day of work.
Also, I have to say, I'm not sure WTF NG is thinking when they hire these recruiters. The recruiter who contacted me was some 25-year old kid a few years out of college who couldn't get a job in her major (finance). I guess she just thought she had a knack for recruiting. She had no idea about any engineering terminology and her favorite catchphrase was, "I understand where you're coming from" (must have said that about 10 times in a 20-minute phone screen).
Her first question to me was, "tell me about your current job responsibilities." Obviously, she didn't bother to read my resume or candidate profile, as I clearly stated in both that I was currently unemployed. As soon as I told her that (about three minutes into the interview), she was looking for any excuse to get off the phone. I don't think she expected me to give her answers like, "yes, I will have no problem passing a background check because of A, B, and C", and, "yes, I am willing to wait up to 11 months for the completion of the background check."