Yeah did all that, and then some... and then I figured it out. Pouring more embarrassment on my self probably, I'll share in the interest of posterity

I went back to the
list of codes and went through, in particular, the handful of codes I had used. I remember how my eyes bulged in delight when I saw all of these "unlock" codes, and stupidly thought to myself, "OH, 'unlock' always means 'good'!" Wrong. The culprit was
#7465625*28638# Auto Network lock deactivated
I was able to reactive this by doing this:
*7465625*28638#
I.e. '#' means 'off' and '*' means 'on'. You want this network 'lock'... I'm guessing this is something the OS uses to gives its networking stack key/code for the transport (or similar) layer of their data network
So I turned it 'on' and all's well.
However, something interesting happened... note that I lost all of my connectivity profiles... even the uneditable ones. I had to create them all by hand and set the browser to use them, etc. And they are all editable, so I put in the homepage of my choice
Of course, the MEdia Net widget (on the TouchWiz) still goes to http://device.home :p