How do we reconcile the fact that Gabriel (peace be upon him) has six hundred wings, each wing larger than the world, with the Prophet (peace and blessings of Allah be upon him) seeing him in his angelic form in this world?

We have not come across a narration that describes Gabriel's wing as "bigger than the world." Rather, what is established is that the enormity of his creation filled the horizon. Narrations stating that each wing filled the horizon are weak or ambiguous, and the stronger view is that Gabriel, peace be upon him, with all his wings, filled the horizon, or that the "rafraf" (a type of cushion or covering) upon which he was, was what filled the horizon. What has been reported describing Gabriel's immense creation filling what is between the heavens and the earth is established. Matters of the Unseen are accepted as they have been revealed, without attempting to qualify them.