Earlier quoted context omitted.
I've done a few rounds of CV edits and reviews early on, it hasn't helped. It's worth noting that the initial CV I had was one where I never had trouble finding work with. Edit: misunderstood "referrals" for "references" so edited my reply out. No, I've never asked for referrals from past colleagues.
Not having LinkedIn is ruining your chances. Candidates without a LinkedIn are going to come across as a scam in the very least, 90% of the time your application will just get tossed if you can't be found on LI.
From where I sit, it's a tool for marketers and recruiters to gather data and it's otherwise completely useless.