Google only takes calls for ad sales and gsuite support as far as I know. Beyond that shaming them on social media is the only way to get their attention. I used to work for a top five web site and even we couldn’t get ahold of anyone - one day Google decided to start crawling us at a rate of 120k rps and it was killing the site by pulling ancient content that was 100% cache miss. No way for us to get in touch with Google officially, our billionaire CEO hadn’t traded numbers with their billionaire CEO so no help there, one of the developers had a college buddy that landed at Google and that guy was able to use some sort of internal mailing list to get them to drop the crawl rate down to 20k rps.
(Microsoft is just as bad - their sales people can’t be bothered to talk to anyone who isn’t a partner, but that worked out great for me, I wasn’t really feeling azure and it made a great excuse to not consider them. One of their sales people did leave me a VM three or four months later but we had already chosen another vendor by then).
Spend ~$5 of Google Adwords, and chances are you'll have someone calling you regularly trying to talk you into using it more - at least that's my experience. In the past it's been a pain to get them to stop bothering me.
If I have an issue with Google, I might try starting an adwords campaign and ask to speak to supervisors when their sales calls comes through, and see if there's an in along the way of "we would spend more, but you see you've done X that needs to be resolved first".
My other approach - not tried it on Google, but it worked very well on DHL and Uber so far - is to sign up for LinkedIn's premium subscription and use that to Inmail a bunch of VPs/SVPs and set out my grievance. My experience so far is that you need to find someone high enough up to be under the illusion - from lack of customer contact - that everything is well. They often seem to be shocked to hear that customers hit the wall, and get approached rarely enough that it's a novelty for them to help out (as such, it'll probably stop working if everyone starts doing this...)
With DHL in particular I got an SVP to get his assistant to light a fire under the customer service operation by telling them said SVP wanted to be kept up to date on how it went, and Cc'ing said SVP and me on the e-mails. A package they "could do nothing about" because it was supposedly on a boat back to the US, magically appeared in my office one business day later after it was located in a depot 5 minutes from my office (I wish I could say that was the first time DHL has told me a package was somewhere completely different to where it actually was)
Thankfully these companies are big enough that the supply of SVPs and VPs is near endless. In fact, with DHL my biggest effort was wading through the list to find the people I thought most likely to reply. Of three messages I wrote, two replied and offered to help.
I worked at large bank where being able to make people wait until end of day or end of week for a reply was a kind of status symbol. My wife needed to do physical therapy after a car accident and rather then letting her take an hour to do that her boss decided to fire her, all the paperwork was sent to London for an managing director to sign. My wife went across the street to a doctor’s office, got him to sign a medical leave application, and walked it to HR office. By the time the MD saw her termination paperwork she was three days into a federally protected medical leave and continued to receive most of her salary for almost a year. She could have worked a full day every day of that time if the bank had made the slightest accommodation, instead they ended up paying for a year of leave. :)
In the past I had written about my experiences with crawling[1], from accidentally getting banned by Slashdot as a teenager doing linguistic analysis to accidentally DoS'ing a major website to being threatened with lawsuits.
The latter parts of the story were when I was part of Common Crawl, a public good dataset that has seen a great deal of use. During my tenure there I crawled over 2.5 petabytes and 35 billion webpages mostly by myself.
I'd always felt guilty of a specific case as our crawler hit a big name web company (top N web company) with up to 3000 requests per second* and they sent a lovely note that began with how much they loved the dataset but ended with "please stop thrashing our cache or we'll need to ban your crawler". It was difficult to properly fix due to limited engineering resources and as they represented many tens / hundreds of thousands of domains, with some of the domains essentially proxying requests back to them.
Knowing Google hammered you at 120k requests per second down to _only_ 20k per second has assuaged some portion of that guilt.
* Up to 3000 requests per second as it'd spike once every half hour or hour when parallelizing across a new set of URL seeds but would then decrease, with the crawl not active for all the month
With some planning we could have accommodated the 120K rps rate and more, but just out of the blue it caused a lot of issues, the database shards for historic information tended to be configured for infrequent access to large amounts of historic data, their access completely thrashed our caches, etc. We did want Google to index us, if there had been an open dialog we could have created a separate path for their traffic that bypassed the cache and we could have brought additional database servers into production to handle the increased load, we even had a real time events feed that updated whenever content was created or updated that we would have given Google free access to that so they could just crawl the changes instead of having to scan the site for updates, but since they would not talk to anyone none of that happened.
I think returning http status code 429 (=too many requests) or 5xx should work. Google claims to respect it. And it's not like they have choice really: the server is refusing to provide the content. Additionally, serving such an error should be as cheap or cheaper than a cache hit.
(Microsoft is just as bad - their sales people can’t be bothered to talk to anyone who isn’t a partner, but that worked out great for me, I wasn’t really feeling azure and it made a great excuse to not consider them. One of their sales people did leave me a VM three or four months later but we had already chosen another vendor by then).