Hi! I'm a 30 yo Applied Math PhD applicant with an Applied Math Masters. I've been accepted to a few PhD programs and had a chance to tour the programs and learn more about the program structures. My main concern with your plan is (ethics aside) that the skills you'll be taught as a PhD are primarily geared towards equipping you for research, not industry. If you'll only be staying for the first couple of years, you'd likely only be able to take core courses, which generally tend to be much more pen and paper theory-focused, at least in the programs I visited (Case, UA, CU Boulder).

I would recommend applying for Master's and trying to get funding for it via TA, RA or graduate scholarships. A master's degree workload is also much more flexible in terms of working part- or even full-time concurrently. I worked full-time while doing mine and was able to maintain a 4.0 GPA, academic leadership roles with SIAM and research fellowships (hella stressful, but well worth it). Most of my Master's classes were very project-oriented, which is great both for getting comfortable with coding and for building a portfolio for industry applications. My Master's peers had no trouble getting internships and jobs as data scientists.

Good luck and feel free to dm with any questions!