All 400 pages of a site are ranked well, but for secondary keywords only!

Hello,

My main site has the following problem on nearly all 400 pages.

All pages of this site are ranked well on Yahoo and Bing for main keywords and secondary keywords too. As about Google, it provides good traffic for secondary keywords only.

For example, a typical page can be ranked in position 1, or 2, or 3 for the main keyword on Yahoo and Bing, but has positions 8-20 in Google. However, for many unexpected secondary keywords, Google still provides good positions and traffic.

In 2012 and 2013, this site was doing very well on Google too. At these times, I build many backlinks for this site using mainly the main keyword and its variations or synonyms.

Since 2014 this site got reduced SERP (search engine ranking positions) on Google likely due to the anchor text over optimization.

What can be done in this situation? I tried to change titles of over 100 pages (using LSIs), and it seems this helped for Google SERPs but only a little bit.

If I try to build new backlinks with plain URLs or brand names, etc. without using main keywords, can it help?

Did anyone manage to recover such sites?

Thanks.