That would be the ideal build, I agree, but I was suddenly reminded of gaps in my badges and was trying to full several at once. If I ever had a need to do AoI again without the goal of Lava Silver, that'd probably be the way to do it... I was gonna say Eagerness Angelic, but I just checked and that's AoI+AoRA N! 90%... I think that one's gonna want Gunrunner not Cateye =P
As far as EE being defensive, you're absolutely correct - offence is often the best defence, especially sub-N!(where stuff you kill rarely comes back - the few viles I encountered this run I assaulted to and burned down with the plasma rifle in a couple rounds). With 2 levels of EE, my chaingun and plasma rifle become significantly more effective. Stack that with SoB like I did here, and even really scary stuff drops pretty fast, saving me lots of valuable health, and additionally avoiding some of the hazards of shotgun style retreat tactics where one often finds oneself backed into additional enemies because the primary target isn't dying quickly enough. Those situations almost invariably cost health I didn't have to spare. Fun bonus: This method also saves ammo. My backpack is full of it not only because I couldn't carry any medpacks or phases, but also because I didn't use much for each kill.
Edit: Actually... after further thought, Cateye sounds like a pretty solid build for Eagerness Angelic. Easier safer distance kills, Int to track down monsters to boost kill rate, not to mention find valuable Invulnerability globes(which seem like the key to this challenge - Nuking a level and surviving gives 100% kill rate for that floor, with no chance of revives), and Scout class to boost speed, find stairs, and make expeditious retreats. I want to try this now... Too bad I won't have a chance until tonight.