O. K. I'll backup a bit....
You mentioned that you set your APN to cellular1wap.I had done the same so that my Third party apps. Would work (in my case Ramble and Google Maps), after that my BB browser started giving me the authentication scheme error followed by the 401 error...The same errors you were getting right?
Since we were using the same network (Dobson) I stumbled on my solution by moving my bookmarks to the "Blackberry Bookmarks" folder...I have no idea why it worked for me, and I was hoping it would work for you .Sorry it didn't.
btw...I still have not gotten a single error since making the change. Sorry It didn't help you i will post more info. if and when I find it.