Hi Mitchell - That makes sense since the error sends in the background.
Historically we logged errors to the db and when we thought the error was going to affect the user, we display an error page with a contact form. We get the id of the error back from the database and fill it into the form as a reference number. That way when the support form is submitted the support team can relay the error number to the relevant parties.
My workaround was going to be to generate a hash of the error or a random identifier and send it as custom data.