Standard clauses CAN be a solution if they address the problems with transfering data. Currently you can't have Standard clauses with the US, because EU citizens have no say against the NSA.
You absolutely can and it's the official solution proposed by the Court of Justice of the European Union since July 16th 2020, date of the Max Schrems II decision.
The court clearly stated that the data exporter has to suspend the data transfer if the recipient is unable to comply with that contract (which must ensure the level of protection required by EU law). This is currently not possible for an US entity in practice, as the court also found, because US law does not grant non-US-citizens actionable rights against US authorities in that matter.
And in practice the website of the Court of Justice of the European Union loads YouTube videos so I'll follow what they are doing as an example and justification.
You can simply sign a Data Processing Agreement (DPA with MailChimp containing Standard Contractual Clauses (SCC) and you're good to go.