I really don't think your question should attempt to be answered in this forum. I have written several posts out here but they were 3 or 4 pages of text. Nobody read them. Christians today like to get small nuggets supporting their view so they can debate it. I am amazed at the responses I get from members out here. Many responses are down right rude and uncalled for. I came to this forum to engage in serious bible discussions. Hardly anyone out here knows the NT Greek. That would take too long as far as they are concerned. So all they can do is read articles from their favorite teacher. Nothing original is discussed, just the same biblical doctrines that have been around since the Reformation.
Sorry for my rant. Ok, let me tell you why I think Covenant Theology is not close to being a literal interpretive method. Most people who hold to the CT position, are Reformed, Calvinistic. they think the reason people go to hell is because of their sins. They are so Reformed that I have a hard time reading from them. To me Calvinism is borderline blasphemy. To CT folks, God has chosen some to be saved. They think we are so depraved that we can't respond to God because we are dead. They have no concept of what the implications of Rom 1. 19ff. They take promises to the nation of Israel, not understanding that the Dispensation of the Jews includes the Tribulation. Some believe that you have to have the works of a redeemed man, and that if they don't they may end up in hell.
Now I don't want to say that you hold to all the above. there are many variations of CT. I will finish this post to you so if you want you can reply to some of it. If you think we are just too far apart to discuss this, then you dont need to reply.