If you think the only alternative to exegetical study that depends on "higher criticism" in reading the Bible is "What does this mean to you?", then you really need to read a bit more widely. I would suggest you start with some of the writings of Brevard Childs.
I've read him. I've enjoyed him. "Higher criticism" uses methods to try and discern what the author
meant when originally writing the material as the basis for interpreting what the text
means for us today. "Literary criticism" uses methods to try and discern meanings from the literature as we have them, and the historical context often has little or no influence.
Canon criticism, which Childs espouses, I think, is part of that. It is not concerned with the original writings, but those writings as we have them in the Canon. For example, as I recall, he doesn't care much about dividing Isaiah into three different books, but studying the book as we have it in scriptures. (One could do the same with canonical Mark with the longer addition.) I believe that he even looks at the order of the books as they were placed in the canon to be significant -- and I think it is, to some extent. There are reasons why Matthew is placed first in the New Testament -- and Revelation last.
Reader-response criticism, which Powell writes about, is another part of literary criticism. It's under this narrow method that the question: "What does this mean to you?" arises -- which I still maintain is primarily a self-study rather than exegeting scriptures. It is a method that can lead to as many different interpretations as there are people in the room. I think that a combination (which is more of what Powell actually does) is helpful. The historical-critical methods, and canonical critical findings, limit what readers may legitimately determine are meanings of a text.