Job posting sites are almost useless for many people at least some of the time.
You ask about callbacks - are you exclusively waiting for calls back? Call the HR managers. I tell anyone looking for a job that there are often more resumes (thanks to electronic applications) than anyone can read. A referral in the company helps most, a face-to-face meeting with someone at the company can help some, but the minimum is the call following up on your application. I called the VP at my current company every week for 5 weeks before he assured me I was in the top contenders and asked politely that I stop calling him. 5 interviews later, I had the job. It was a process.
Linkedin and other professional networks are much more useful than most job sites. If you know anyone in the field outside your current company, who you could call and ask for referrals or other options, it may be worth asking around to see if anyone has anything they can offer or recommend. That's usually much more valuable than firing off applications to job sites. Former supervisors, colleagues with your company who moved on, anything.
That said, 35x current living expenses will be more than 60x current living expenses in the decade you described... if you do nothing. I get the impression that your conservatism is not negotiable, but if you got a job, any job at all, that paid the bills today and which wasn't making you miserable, you'd be ready to retire with more than your projected requirements without saving any more anyway.
Can't comment on parlaying to other engineering roles, though - not an engineer.