How long before I should change job hunt strategy?

Some starting info:

• Master’s Computer Science & Engineering GPA > 3.5
• Bachelor’s in Business
• No internships, was a teaching assistant , performed minor research experience (two baby summer projects)
• Graduated May 2017
• Hunt Started: Late May

It’s been almost 3 months and I have not received any human replies, and I’m starting to think I should change my approach.

I’ve reached out to Google and Apple recruiters through referrals, but I was late to the game and the summer intern positions had already been filled. I’ve applied to a few other major software companies, but have not heard word back. My wife thinks I’m being overly anxious, but it’s my personal inclination to hope for the best, and prepare for the worst. I understand that the summer is slow, but I’m hoping that as September gets closer, things will start to pick up.

Our current living situation is financially secure, and does not require me to work, but I really want to (which is why I retrained in the first place). So I thought I could be a little picky. I want to work on interesting problems like those I came across in my grad classes, but I've found that many industry positions are exclusively for PhDs or MS w/5+ years of experience. I’d like to believe there’s somewhere I can fit into, but I can’t seem to find anything.

I see quite a few devops positions(which most of my peers went into), but I worry that I could be pigeonholed into devops, which does not seem like something I would be interested in long term.

Currently, I’m spending my time learning C++ with a personal project based on some of my research before graduating.

So I have a few questions on my mind:

1. How long before I should suck it up and begin applying for less ambitious SWE positions/ Am I being too anxious?
2. If I really wanted to work in fields like Machine Learning, Distributed Computing, or Operations Research would pursuing a PhD be the only way?
3. Should I consider applying for devops positions with the hope of quickly (1-2years) spring boarding to a SWE role?

Thanks!