Have you tried using a monitor IP on the gateway? If you set a gateway to "monitor" the IP of the opposite gateway, does it still do this?
These are DNS servers, not ping servers. I would suggest to not (ab)use public DNS for ping tests. They will eventually rate-limit or block pings when you do this.
It's not just about bad etiquette. Google seriously DOES rate limit these pings. I have been debugging multiple boxes where using 8.8.8.8 for monitoring caused intermittent "gateway down" issues. And I am not alone. I have also seen a local ISP with couple of thousands customers redirecting all DNS queries to Google -- because their servers broke down. Well, it did not work exactly well. https://developers.google.com/speed/public-dns/docs/isp