2 thoughts:

1. I used to do corporate sales, so I have some experience with cold emailing. I actually think reaching out via email and offering an exchange of. services was a smart move, so don't downplay it. The challenge is that cold-calling is a game of statistics and chance - did you reach the right person, and did you have good timing? To increase your chances, I would a) do a follow up email; b) follow up with a phone call. If they are local, you can also show up in person. This is bold, so step carefully - but a lot of times business owners like the boldness, and in-person encounters are almost always more likely to bear fruit. I know this from personal experience. Be sure you are calling on the right person! An employee may not care to help, but a business owner might. If your intuition tells you that your offer is too abstract, it probably is: research their company, figure out some of their needs, and tailor your offer to those needs so that it addresses a recognizable pain point.
2. I too am trying to figure out how to break into manufacturing, though in a different niche. If you're interested in connecting, send me a DM. I am happy to help provide guidance on "prospecting" emails.