The PhD shouldn't be a cause any issues, just show it is recent. The fact it isn't in engineering/comp sci won't help you get in the door but it shows you can

The PhD shouldn't be a cause any issues, just show it is recent. The fact it isn't in engineering/comp sci won't help you get in the door but it shows you can complete a difficult task. I'd highlight on your cover letter how you feel your experience with your PhD work is relevant in terms of software to where you are applying. It will probably be harder for you than some others, but I don't think if you are decent skillset wise where you'll have major issues. I'd look for jobs where you are sending your resume not to HR but to the hiring manager directly ideally. HR is a filter, and it is hard for them to know what is valuable or not and so they use things like the lack of a degree or relevant work experience as the first filter, understandably. Hence getting directly to a hiring manager will be better. Also, you might ask some of your professors that may have contacts within the field or maybe they can refer you to a CS dept prof that can help you. Getting a warm intro to a company wouldn't hurt you. A little networking could go a long way here.