And even though that seems like a large distance, it is a very small redshift compared to the total time the universe has existed. The cosmic microwave radiation background, for comparison, was emitted at a redshift of about 1100. So a redshift of 11 only covers 1 percent of the expansion of the universe since the CMBR was emitted.
> we've seen 97% of the universe's history
No, we haven't. See above.
> Including the microwave background in that pushes the number to 99.997%.
No, it doesn't, because even though we can see the CMBR, we can't see anything useful in between its redshift and the redshift of 11--not because there's nothing there, but because what's there is too distorted and faint to see. (The only reason we can see the CMBR is that it's black body radiation at a temperature we can independently predict from our knowledge of the physics of recombination, so we can tailor extremely sensitive instruments to looking for its precise signature.) So there is a lot of universe that we haven't seen.
No we have. See above: While redshift goes all the way up to infinity, in terms of cosmological time, there's still only 0.4 billion years between z=11 and z=∞, or about 3% of the age of the universe.
> if our models are correct
What is this whole discussion about?
You're arguing a stance that assumes the model is correct in a discussion about the risks of assuming the model is correct.
But trust me - our model is not correct.
In terms of time, yes. I was thinking in terms of observable spacetime volume. Even though there's only about 0.4 billion years before z = 11, the scale factor increased by a huge factor during that time (a factor of 100 from CMBR emission at z = 1100 to z = 11). That's a lot of spacetime volume from which we have no useful observations.
You might as well be looking at a single frame of a movie and telling me you know the whole plotline because it happens to have the same pixels on screen for the whole shebang.
We have a sampling of data from 99.997% of the timeline — but the sample itself is extremely sparse.