Is it possible to suppress the "signed-by" and "mailed-by" headers that sendgrid adds to white-labelled mail? (Paid account.)
Is it possible to selectively suppress them on some mail and not other mail?
No. It is not possible to selectively suppress the mailed-by and signed-by headers unless and until SendGrid provides such functionality which I don't think they will. There is currently no way to even suppress those headers for all your emails, as far as I can determine. It appears that SendGrid ALWAYS includes those headers and does not provide a way to turn them off.