GDPR has data portability rights that include the right to ask the data controller to transmit your data to another, if "technically feasible".
It's implied that the importing side will make this work on their own since they only benefit from allowing data imports to onboard new customers while the exporter is losing their customer.
Article 20, Section 1 states:
The data subject shall have the right to receive the personal data concerning him or her, which he or she has provided to a controller, in a structured, commonly used and machine-readable format and have the right to transmit those data to another controller without hindrance from the controller to which the personal data have been provided[...]
Separately, Article 2 states:
In exercising his or her right to data portability pursuant to paragraph 1, the data subject shall have the right to have the personal data transmitted directly from one controller to another, where technically feasible.
This part specifically mentions the controller you originally gave data to, but says nothing about whom you now want to import it to:
> without hindrance from the controller to which the personal data have been provided
> For especially severe violations, listed in Art. 83(5) GDPR, the fine framework can be up to 20 million euros, or in the case of an undertaking, up to 4 % of their total global turnover of the preceding fiscal year, whichever is higher.
> “the concept of an undertaking encompasses every entity engaged in an economic activity, regardless of the legal status of the entity or the way in which it is financed”
These services have no economic activity whatsoever, or if they do it's in the forms of donations to keep the lights on. Who do you propose that the GDPR hammer strikes?