You currently have 3 h1 tags which I wouldn't recommend, especially for such terms as "request a call back" and "nationwide servicing" they don't really represent a focus and look to be sitewide h1's from your sidebar.
8 Alt tags missing from images on homepage, minor but still worth resolving.
No implementation of schema markup/micro data. Especially on product and category pages.
No contact address, no Google maps/business listing to show its a tangible business. Addresses and citations provide trust signals which you lack considerably. Take a good look at your competitors and identify what they have done that you have not.
You have very few backlinks that are note worthy, although I can see an effort to gain better backlinks of late I still wouldn't consider those to be fantastic, I suspect alot of your problems stem from your past, the masses of low quality, spammy backlinks that you had previously in the last 12 months may hinder your progress going forward. Did it result in a manual penalty ? Have you recently done a disavow of backlinks in the last 12 months?
You certainly need to start building, quality, related backlinks and make 100% sure the poor quality has been dealt with properly.
Do you have access to search console ( webmaster tools ) and have any manual penalties been raised ? currently and previously ?
Page speeds and user experience
Your page speeds although read ok for physical page speeds, are not so great as perceived ( user experience ),there are a number of things you could do to help your cause, especially image optimisation. They might be considered small wins, but it all helps when you are struggling to make progress.
I think you'd benefit from an overall search and social strategy to tie into your current PPC activities and external shopping integrations ( amazon, google merchant, ebay? ) , I think a better focus on quality and authority brand building is what is really required to pull some trust back.