The key part of this is that you need to add your routed email address as a new account in gmail, uncheck "treat as an alias", and then use a Gmail app password in the "send as" details for SMTP.
Create a new app password here
Finally, you need to modify the SPF record to include Google:
v=spf1 include:_spf.mx.cloudflare.net include:_spf.google.com ~all
And set a DMARC record:
v=DMARC1; p=none; rua=mailto:<your-email-to-report>
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