Interesting in that you wound up with the 800mm 5.6 as in my local birding community most bird photographers wound up acquiring the 500mm. And I would agree the 13k seems a bit over the top. Are you hand holding that 800mm lens or using a tripod/gimbal combo?
Congrats on the 1DX as well.
I have tried a 500mm but find it a bit short, even the 600 needs to be close to minimum focus distance if you like to fill the frame with smaller birds. Where I go birding the 500 F4 is probably the most sought after lens, probably due to it's lighter weight and price though those that have tried my 800 hate me! Especially when they learn what it cost.
My 800 is normally on a Gitzo/Wimberley setup though it is OK on a mono pod and can be handheld (for short periods) if necessary. If hand holding then keepers start from a shutter speed of 1/125th or faster - it has 4 stop IS. Some say it is too big and too specialized - I disagree, I even store my camera on this lens as it is by far the lens I use most!