I love that piece. I've always played it as written, honoring the split, as you say. In the late Brahms there are a fair number of places in which he seems to have intended a fingering that might not seem like the most obvious or easiest, like this passage, or several with interlocking hands, and I think he was aiming for a specific effect, so I stick with what he seems to have wanted. Still, he wrote for his hands, not yours, and if you get the sound you want, why not adjust the fingering.