I think one of the problems as processor is to be sure that if for any reason US government ask to access this data (of which we are controllers) then you have the means to refuse as they are protected under GDPR.
The GDPR specifically allows for MLAT treaties to be used when requesting the data, without notice being provided to the customer. The US has this agreement with many European countries but not all. This also only deals with PII from members of the EU and not run of the mill data and/or data not concerning EU members so the situations will vary depending upon the target of the data, the request etc. While I cannot give exact numbers, and it doesn't bypass the fact of the GDPR, but we deal with very very few such requests in general, and I can only think of a hand full that would revolve around EU data.
One also has to consider the CLOUD act which has passed in the US. This is what we are waiting on resolution for concerning any GDPR compliance. As it stands, any US company, be it Microsoft, Google, Facebook, Amazon, Cloudflare etc, regardless of where the data is stored around the globe, must disclose it if the criteria of the CLOUD act have been met. This does put sections of the GDPR at direct odds with US law and any company that has headquarters or a significant branch within the US (Basically meaning there's very few companies globally that aren't impacted by this). We expect this to be addressed between the EU and US with a special agreement in this regards but only time will tell.
We do treat our customers data with the utmost respect and our internal policies do align mostly with the GDPR especially as a processor we will continue to evaluate things. I do anticipate the Privacy Shield to be in place before the 25th of May and/or shortly there-after. We'll likely do a forum post or similar and Privacy Shield details will be listed on our website, privacy policy etc.