I agree with moczys, contacting firms directly is probably a good way to go. I think a lot of design consultants do need a jack of all trades, and you might just fit the bill for the firms needs even if they haven’t advertised yet. That’s how I got my job (I’m your mirror image, an industrial designer who can pretend to be a mechanical engineer) - a small ME firm was considering a project that required some ID and I just happened to contact them at the right time. I’m not saying happenstance is necessarily a good job search strategy, but you might at least get a good conversation with some of the firms out of it.
I know less about corporate gigs, but even though you may lack some of the specific qualifications I wouldn’t shy away from jobs you might be interested in. If you can get past an HR gatekeeper there may be some who are interested in getting some variety of background on their team. You’d might fit best at the fuzzy front end of R&D at some places if you can find those departments.
Regarding your skills, I’d make sure to brush up on at least the basics of designing for injection molding and other plastic processes (even looking on injection molders’ websites for their guidelines is a start), and try to learn some CAD surfacing and learn a little about curvature continuity. As a designer I cringe at the thought of anyone creating final CAD of a form without the ability to realize the subtleties that can really make a design shine. Not all roles require this, but it seems like the roles you are looking for might.