The problem isn't non EU services, it's the US CLOUD act
Other countries have legal systems which are considered as offering equivalent protection:
> The European Commission has so far recognised Andorra, Argentina, Canada (commercial organisations), Faroe Islands, Guernsey, Israel, Isle of Man, Japan, Jersey, New Zealand, Republic of Korea, Switzerland , the United Kingdom under the GDPR and the LED, and Uruguay as providing adequate protection.
And for many more countries standard contractual clauses would probably be enough