I thought I'd come back and provide my results for the sake of anyone else who might run into this.
I was already thinking along the same line, so after your nudge I went ahead and pushed the update. After the device rebooted, I received a message that said there was one more step to get the device ready for windows 10, and that they would take care of it if I just connected to AC power. I did so, the device was configured and I was then able to download the 10581 update. I did so last night, and so far everything is really smooth. A few quirks, like occasional flickering and the Samsung WatchOn app doesn't work (which wasn't unexpected, since it's a Lumia software build and the Icon doesn't have an IR blaster. I never really used that feature so it didn't matter to me but, if for whatever reason, you can't live without that feature, that's something to think about. Also, I'm now not getting any haptic feedback when pressing the keys to the left and right of the home button. Again, insignificant and I'll gladly part with that for Windows 10, just wanted to be thorough. A huge thanks to you, Asellite, for taking the time to compile the work of those who discovered this method (a huge thanks to them as well) and composing a guide so easy anyone can follow it. My Ativ SE is in your debt.