I wonder if you are less impacted by the lack of CS degree than by your "Software QA Engineer" label.
My own experience was that my initial position as a software performance engineer resulted in a perception that I was a "tester" without technical skills despite having multiple CS credentials and published code in practitioner-oriented sources.
Overcoming recruiter biases was such a struggle that I now routinely counsel students and early career programmers to carefully consider whether job role perceptions would negatively affect their future prospects. I also tell them, when financially viable, to not take on roles where hiring orgs cannot give them a day-to-day job description that directly matches their desired career path.
This advice seems quite challenging or maybe misguided for data science careers though. It seems like just getting an entry-level data science job might require a dedicated MS in either CS or stats, with a healthy set of projects in whichever of those two subjects you didn't spend grad school working on to prove yourself . . .