That's a valid point about complex parsing. I remember being very concerned about adding unnecessary overhead to each packet during encapsulation.
As for the SG, it primarily authenticated the Xbox machine account using Kerberos and then maintained a security association, accepted heartbeats, authenticated and decrypted incoming ESP-UDP packets into IP packets that it forwarded to the backend servers. Responses from the backend would be encrypted, authenticated, and encapsulated before sending back to the Xbox. I don't think the SG had any knowledge of higher level connections running through it, such as TCP or HTTP, so it would not have manipulated HTTP headers as they passed through.