We are not being seen for our main keywords in the front of our title tag. No matter what we try, Google robots ignore our main keywords. We are seen for other keywords and we are on page 1 of Google for those. Those keywords are in the domain name. Can we create a folder and place the index page in the folder? Will Google spiders see it and index it correctly? Here is an example:
Xerxes, I doubt if "website" is the killer, though anything is possible. I think you are too focused on keywords in the URL - get your keywords in the title, headings, and text, plus, of course, your link text.
At first glance, it sounds like your problem is link text related. Your higher ranking pages may have good links like "widget sales", while your home page may have just "home" or "XYZ Corp".