Hallelujah. HALLELUJAH! I got it sorted.
I was wrong about the drain pipe exit, it was sitting exactly where it should have been, just the grass had completely covered it.
The drain snake had hit the root system so hard it was basically impossible to get out. I had convinced myself it had twisted itself into a knot, was trying all sorts of insane **** with vice pliers and whatnot, it turns out that was completely unnecessary.
Once the water heater was flushing cleanly I used the hose shoved it up the outside drain pipe. Turned the water on full blast, and to my amazement, the water started coming out into the water heater basin; The clog was clear!
Once I managed that I could pull the drain snake out.
Beware anyone using a drain snake, it's not a trivial matter to use one of these, and if you **** up, you can be in for one HELL of a rude awakening. It takes skill to use one properly, and a good plumber will have that skill and know what to do. Not saying don't use it, just don't be an idiot and stick it on a drill at full speed thinking it'll just do its magic.
Our water is not too hard, but I have occasionally drained off some sediment from the bottom of the tank. Never replaced an anode. Not sure if it's true but I always figured the chance of something going wrong like some threads stripping or something breaking was high enough that I was better off leaving it alone and waiting until it failed. I'm usually a big preventative maintenance type of person but sometimes I worry about the unintended consequences. I suppose if I was disciplined enough to really stay on top of it there would be less chance of things seizing.
I get that line of thinking, but I've learned it's never a good idea to get intimidated by a job. Dig in hard, go deep, you'll figure it out along the way, and then you'll get it sorted how you like it.
ALL of this said... I think my water heater might have a leak in it, and it's even possible I caused it. Obviously I hope not... but I'll have to investigate.