To add to the many informative answers here...I would like to say...start looking at utilizing your website for the relevant long-tail keywords.You can get 100's of long-tail keyword terms that are less competitive and 100 long-tail keywords X 2 visits per keyword term = 200 visits rather than 4 highly competitive keywords x 2 visits per keyword = 8 visits.
I mean start attacking from a wider angle rather than a narrowed approach. Utilize your website for the long-tail keyword combinations as well as for the highly competitive keywords. One will take time while the other will help you in your journey to get there.
Also ranking for a keyword does not always mean that you are getting a targeted audience. You might get a good traffic but does not mean that it will end in conversions. So instead of only concentrating on Organic traffic, also look at other ways to drive RELEVANT traffic to your website. And, get creative with online and off-line marketing convergence [eg:- Bumber stickers with your URL, T'shirts with your company name & URL etc. or if you want to be more creative...think about the prospects of AR (Augmented Reality) when it comes to convergence].
Also, remember that your company employees with their social network presence (Be it Linkedin, Twitter, Facebook, Pinterest etc. are your immediate Online marketing and off-line partners. They can spread the word around their families and friends and the social media network will keep on multiplying. So, leverage them in that area and also put Bumber-stickers on their cars (or whatever other creative stuffs) and on their friends and family members cars lol.
And, when it comes to creating awareness among your target audience, Organic traffic is not the only way...it's just one of the ways. Use other online tools, websites, promotions etc...basically mix it up with a good SEO technique and Online marketing/branding/promotion activities.
And, ultimately it all depends on what USP and value you are providing through your website and through your off-line point of purchase. So, think about how you can provide value and engagement.
Anyway, coming back to your point...I guess it's high time that you start educating your boss. I understand from what you've written, that his SEO or Online marketing knowledge is not much, and that is where you need to be strong (and soft at the same time) and educate him. Go armed with all the knowledge you've gathered from here lol. And, never give up!