The mission office won't be able to do anything, unless the account is [area numbers] @ missionary.org. If the email in question is [yourname] @ missionary.org, you will need to contact the missionary department support at gsd-missionsupport @ churchofjesuschrist.org since you'll no longer have access to their support website.
The problem you're experiencing is that you created a Samsung account with your missionary email, which appears at the top of the Settings app. A Samsung phone cannot be factory reset unless the Samsung account is removed. Since you no longer have access to the missionary email and you likely didn't add another recovery method, you can't reset your password or receive TFA messages.
If you have the lock screen PIN and can get into the phone to put in a Wi-Fi network, then they might be able to remotely reset it for you. Otherwise, they may be able to reprovision your missionary email account, which will allow you to receive emails sent to that mailbox, but all previous emails, Photos, and Drive data would be gone. Best of luck, let us know how that goes
