Hey @Nic_Oliver, I can see how shopify app execute would be useful for extension-only apps where you don’t have a backend to run queries through. That said, mutations via shopify app execute are limited to dev stores regardless of permissions, so even without the org restriction it wouldn’t have worked on your client’s production store.
For that bulk export, the Bulk Operations API is the way to go. Your app is already installed on the store via custom distribution, so you have an access token from the OAuth flow that you can use to call bulkOperationRunQuery directly.
On partner/collaborator access to client credentials, I’ll pass along the use case of extension-only apps needing to run one-off queries against client stores. As always, the developer changelog is where any movement on that would appear.