Howdy, There have been a couple of ipe bows posted here that were only 3/4" wide. I've made a couple of narrow ipe bows as well. Ipe, of course, is much denser than oak, but the whole stability end of the question is still proven. As long as the bow has a little string follow and is no thicker than it is wide, the bow will be stable. Problems with stability should ( in my opinion) only arise if the bow is reflexed, recurved or thicker than it is wide. I believe the chapter in TBB on african archery describes bow that were round in cross section.
The big problem with a narrow oak bow is that it will probably take a lot of set, though a longer bow would minimize the set.
Ron