OK sorry for delay. Digging into this one now.
Your client is ranking #2 or 3 most of the time, not bad. But he could easily be #1 with a little work.
There are 2 main competitors above him A+ and 4 Affordable. Both are outranking in part due to violating guidelines.
You said: "The top 2 spots are businesses much further from city center point, these listings have not been claimed and their websites are not optimized in any way."
Maybe I'm seeing diff results but the top 2 I keep seeing both have claimed listings. Plus 4 Affordable site is built by SEO company and IS optimized plus has tons of backlinks.
A Plus has a major violation that's helping him rank. Name on Place page is just Lawn Service.
https://plus.google.com/110833900270255427365/about?hl=en That's just keywords, not his real name. You could do a map edit and change to the real name and it would get approved. (Don't be logged into client's account as the name could show on the edit and you don't want his name to show.)
4 Affordable that usually often outranks your client has major violations. AND city in cats is part of what's helping him rank high.
https://plus.google.com/102156421525689202186/about?hl=en I'd try doing a user edit on maps and change his listing. (Don't be logged into client's account as the name could show on the edit.)
Plus I think they both are home offices and are in violation for showing their address. I have NO problem editing KW stuffed listings that violate the guidelines. I think of it as helping to level the playing field and clean up spam. BUT if you report them for violating the hide address rule they will get deleted. Even though it's a guideline violation and even IF I wanted to knock someone out of the rankings,
I personally could not do that to someone after all the pain I've seen it cause in the Google forum. But they ARE in violation and COULD eventually get removed by Google even if you don't turn them in..
Backlink comparison:
http://img1.uploadscreenshot.com/images/orig/7/20202485235-orig.png
4 Affordable has a TON of backlinks.
BUT HERE'S the thing - if those guideline violations were cleaned up and if you just did some good solid onsite LOCAL SEO with all the right Local hooks that could push your guy right to the top, likely even without building backlinks.
There a lots of problems and missing elements with the Local SEO on your client's site. Granted the other guy's sites aren't ideal either, but totally optimizing this one I think would make all the diff.
I train hard core highly skilled SEOs all the time that say I backlinked the hell out of this listing and built a ton of citations and I can't get this client to rank. I do my Local SEO training and show them how to REALLY optimize a site for local search and that's the missing piece of the puzzle.
If you take my Local SEO course I'll show you some tricks that will really help this one AND your other clients as well.

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