Is there anyone you worked with before who is now employed doing something you’d like to do? Have you tried asking them for a referral? Referrals from former coworkers are vastly more important than your resume.
To your suggestion: nearly all my coworkers from all my former jobs are academics, with permanent positions at their home institutions. That hasn't stopped me from reaching out, of course, but by this point I've worked my network as much as I know how to do, and while it's gotten me a bit of interest, it hasn't gotten me anywhere substantial.
I do appreciate your mentioning this angle. I'll have another look through my alumni directory, LinkedIn, etc. and see if I've missed anyone.
Automation engineer > software engineer > job
Also suggest joining local and tech focused slacks, as it seems a lot of jobs come across those nowadays.