Managing personal Outlook.com account settings, security, and privacy
@Kornelijus Perlys said
Could a moderator please guide me on how to reach the Account Compromise / Recovery team directly when the support system is blocked?
There is no such Support Team. Microsoft Account Security is an automated process. Microsoft Support Agents can not unlock an account, reset your password, or change any Security Settings no matter what documentation you can present.
I know my original email, former Gamertags/Minecraft usernames, and previous passwords
You can try the Xbox Account Recovery Form
https://support.xbox.com/en-US/forms/recover-your-microsoft-account
Or the Microsoft Account Recovery Process
https://support.microsoft.com/en-us/account-billing/help-with-the-microsoft-account-recovery-form-b19c02d1-a782-dee6-93c3-dc8113b20c42
But if the hackers have reset your account info/security settings and have enabled Two Step Verification, the account is lost and can not be recovered.
I am sorry. I know that losing access to your account is more than just an inconvenience, it can cause real hardships. I wish I could give you another answer.