It's always tough trying to explain to someone that it just takes time with a new site. The best way to show this is by using http://www.opensiteexplorer.org/ and showing the the metrics (inbound links) of the competition for the main keywords.
For example, with a quick look using http://ahrefs.com you can see that you only have 5 inbound links to your website, where movingdayboxes.com has 1,513 (as seen in Open Site Explorer). Once OSE indexes your site, you can start monitoring your metrics (there is a new update today, so you may be in there later).
It isn't your ecommerce platform, and Authority Labs is just another tool and there isn't anything out there that crawls as much as Google does. They all just crawl portions of the web.
Now your bosses response will be "Then we need to start building links". Be very careful with this and start smart and tell him that it is a long term strategy starting with your local market.
If he is looking for instant results, then PPC is the way to go.