Have you considered a PhD in Electrical Engineering? If not, why not? I know it is a common trope on here to "want to do research and not product development". I often wonder how many of the people that say that actually have product development experience (let alone research experience). While the grinding pressure of high-volume products didn't turn out to be my cup of tea I must say that I have had much more personal satisfaction doing advanced development than I ever did doing research.
While I enjoyed my time in research (I will define that as activity for which the final deliverable is a conference or journal publication... or even an internal report) I am much more excited about my time in low-volume advanced development. Basically, you have a significant problem to solve in order to advance the state-of-the-art in some area and you have to figure out how to get it done by hook or by crook. It's a blast. Also, I get immense satisfaction knowing that systems I helped develop are on the front line of cancer, pharmaceutical, and materials research. And I still publish a paper or so a year.
My point is to have a look around before you get too focused on roles and what degree you should have for what. There are a lot of amazing opportunities out there and you can contribute in a variety of ways. There are some areas in electrical engineering where a PhD is a big plus and more importantly the jobs available for PhDs tend to be more interesting (in my opinion).