We would post the exact same blog to similar blog hosting platforms
Care to give examples of a few "blog hosting platforms"? Because I have a feeling that you're referring to websites that are known in the SEO world as web 2.0s, which are not useful at best and detrimental at worst.
Also, by "solar company" I assume you mean "solar panels company" (so, probably a company that either produces or installs solar panels, or both). And the reason I'm saying this is because if you can approach your company's activity / profile from a controversial or groundbreaking angle you can run a pretty successful PR campaign in your local area (or the area in which your company operates). I'm not sure that solar panels can have anything controversial or groundbreaking about them, but you know better so you'll be able to tell whether a PR can be good or bad.
Regarding the backlinking strategy, the most valuable backlinks today are PBNs (that is, your own private network of sites that you have 100% control of), guest posts, and niche edits (link inserts).
The most powerful backlink method is definitely your own PBN first, or purchased / rented PBN links second, but only as long as the PBN is quality (you will have to do a lot of reading and research on what constitutes a quality link in general, and a quality PBN link in particular, or else you'll get scammed)
If PBNs are out of your reach then the next best thing are niche edits. But again, only as long as they're quality niche edits (quality niche edits in this case means that your links are getting inserted into aged articles that are at least slightly relevant to your niche, and those articles are already indexed and ranking in google and get decent weekly traffic).
If you can find, let's say, 10-20 such quality link insertion opportunities you have a good chance of your domain getting boosted in the SERPs, but expect to pay $1000s for such links. And they're rare, too, so you'll probably need to have a reliable source of them, or get them through a SEO agency, which might cost you even more. That's why the most popular links on the market today are guest posts, but again, only as long as they're quality ones, otherwise there's little difference between them and web 2.0s.
Regarding your blog... yeah, it's a good idea to have a blog attached to your domain (or hosted on a separate domain if you want, but I don't think it makes much difference) and post to it regularly (weekly is fine, 2-3 times a week would be even better if you have a big readership and can find lots of topics to talk about)