Will I really lose access to my account if I don't verify by January? 
Yes, that's why you have to comply to KYC to verify your account so do it before the deadline.I refuse to upload my documents because I was told I would never have to do so. I guess they lied to me when I signed up.
It's not a lie but how stakes have to comply with every rule of the license where they are registered.
KYC will always be an unpleasant thing to do but unfortunately you are almost impossible to refuse it, if you refuse to do it at stake and move to another casino it's only a matter of time until you too have to be faced with the choice to do KYC.