I wouldn't say I have given up on Google. Rather I believe what I do for Etsy searches works for Google as well almost all the time.
I also view it as more of a rate of return question. I have limited time since I have a full time job in addition to my shop. Spending 2-3 hours a month working on revising any poor performing listings from an Etsy SEO perspective and writing good descriptions as I list items has netted me daily sales from Etsy as a relatively new shop. I do get regular daily Google views as well and also a few sales a month as well from Google. I also will get occasional wanelo, facebook or pinterest sales and right now do not spend much time at all on those venues.
My point is that doing well on Etsy search results is simpler and more formulaic than getting a good result on Google. And the efforts I put forth just to develop good results in Etsy will 98% of the time also be good for Google. The same can not necessairily be said for shops that focus on optimizing for Google. Shops optimized for Google that ignore Etsy search tag and title formulas will generally perform poorly on Etsy searches.
For Etsy, I focus on good titles and matching tags and good listing descriptions. Thinking of niche keywords to use. Those all are Etsy SEO but those niche phrases get carried over not just to Etsy but to Google. When I prepare a listing, I work it for Etsy search because it is a smaller world to work in. But those exact same issues I work through on a listing are also good for Google and will get me seen in those niche searches on Google without me spending hours thinking about it.
I could blog and do any other number of things to build up my backlinks and reputation and worry whether or not Google will see favor as different than favors, but that would be several more hours a month in order to see even a small increase over what I am already doing.
In the large world of jewelry, I focus my time on developing new listings and doing quick checks on my Etsy SEO to get a much higher return here. I spend time trying to improve photography and filling orders and good customer service. That success does trickle over to Google without putting in as much effort as most people seem to think.
Right now, for me personally, all I focus on is Etsy SEO and then very basic Google issues (i.e. section titles, shop announcements). That gets me excellent search views from Etsy on a daily basis as well as sales and also regular Google views into my shop and occasional sales. The work you put in for Etsy searches and good listings should also do reasonably well with Google if you've done them right.
Again, that's all just my experience. If I had more time, yes, I would do blogs, etc. But if I'm a struggling shop, I think the best place to start really is to focus on Etsy SEO. Again, that's just my personal experience and other shops I know as well. There are always multiple paths to success.