Ask HN: How to Transition from Marketing to Product Management?

Context: I'm a former mechE (engine component design / test / mfg) who went to b-school and got into marketing (ad-tech and later developer marketing) who wants to switch to Product Management (because I want to make a bigger impact on the actual product - instead of just talking about it). I can code (Alexa skills / Python / JavaScript). I can write well (about software and other things!). I get shit done.

But here in NYC's tech scene, I'm an ugly duckling. Employers assume I'm too expensive ("oh, he'll want a McKinsey salary"), too inexperienced (no formal product experience), or _too_ experienced (he'll never want to do this job - it's too entry level - he has an MBA). And that's at both the associate/junior and regular PM level. One thing I hear over and over is how "unique" it is to find a candidate with both engineering & marketing experience -- but perhaps that's code for "your career history is all over the place."

So, what can I do to better market myself / convince HR & hiring managers that I'm a quality candidate? Should I take my MBA off my resume/linkedin? Should I get a PMP certificate to prove that I understand gantt charts? Should I say fuck it and start applying for dev jobs?

Appreciate the hive mind's advice :)