If I were in your shoes I’d look for a program to get a masters of ID, maybe taking evening classes here and there as it fits in your schedule. Having an ME background is incredibly beneficial to ID, but to really become a designer I believe you need to learn not just the “hows” of production that they teach in school, but also the who/what/when/where/why through studios and design history and research coursework. I’m an industrial designer and I work very closely with MEs and sometimes we do incorporate their design input, but at the end of the day the designers call the shots.
Here’s something else to consider (although it probably doesn’t apply to dedicated ID firms, I work as one of a handful of industrial designers at a huge contractor): When potential clients come to our company with a project, they ask for a stack of resumes for every employee who will be working on their product and they want to see designers with design degrees. They would balk at the fact we hired someone and gave them a job title of “designer” even though they have no formal design education, and might take their contract elsewhere.