Hi Stephen,
The link removal requests may help you clean things up somewhat, and hopefully the new site will improve engagement and conversion rates (both highly important). Blog posts can also be a very good thing, as they increase the amount of relevant content on the site, fixing the technical errors should help search engine crawling and indexation, and on-site SEO is always a helpful place to start. But on-site will only get you so far.
Looking at your blog, it seems that each post is tweeted about once (except the latest, which has two tweets) and shared on Google+ a couple of times. You also mention you have not built any new links recently, so your problem may be less about what you have done in the past and more about what your competitors are doing today that you are not.
If your competitors are running PR or marketing campaigns which earn them links and are using social media to reach out to more than a handful of people they will be gaining authority while you remain static. Definitely continue with your link removal requests - and disavowing of links after a week or two if you don't hear anything from those directories - but also think about moving forward: put together a marketing strategy that includes digital, build up an editorial calendar, and work out how to use social media effectively (for example you could send Tom White an email next time you blog about him, or tweet the people your reps meet at Silverstone with things they might be directly interested in).
Build things that people will want to share - whether that's an infographic or a video of you working with a couple of other small companies to build a Rube Goldberg machine filled with your nuts and bolts (Honda did a whole ad based around sprockets and bits of windscreen wipers). Tell people about those things and work with other people who will also get the word out (this is called fusion marketing and can be a great way of getting yourselves out these). I know what you're likely to say about being a boring industry, but to head that question off at the pass I'll direct you to Ross Hudgens' recent webinar Content Marketing in Boring Industries. In short, take where you are as a standing point and think about how you can start running - rather than looking over your shoulder at Panda, Penguins, and other animals from the Google zoo.
Hope that helps!