Richard you pretty much hit the nail on the head. If your listings are congruent across multiple mediums it appears that google will recognize your listing as being the most relevant.
In addition to that you need to
Complete your profile - images, videos, hours, payment methods, etc...
Build some links with good anchor text to your map listings. Including passing some link equity from your main website back to your map listing.
Make sure when you are syncing up there is a link to your website in your example.