Her archaeology didn't pick up any post Smith Doctors either, that's an immutable problem with Doctor Who, with all these different versions of the same person running around through time and space it's amazing they don't encounter their future versions more often (or maybe not, space is big, really big, after all and when you factor time into the equation...)
Also you're assuming River has no knowledge of pre Hartnell Doctors, you can't prove that (spoilers!)
There's nothing to suggest that River's DNA works exactly like a regular Timelord's either, she's (apologies Alex) a freak, a mutation, and as far as we know she only regenerated a couple of times. Maybe she only had enough energy left to regenerate one more time or maybe she scarified 400 future lives to save the Doctor, we just don't know, but nothing in her creation is necessarily contradicted by the Timeless child. There's more than one way to skin a goose and maybe more than one way to bake a Timelord.
And I say all this as someone who isn't the biggest fan of the Timeless Child storyline.