You don't get to assume spherical cows in a vacuum on this one.
One interesting study of radiologists showed they actually fared a bit better than people without that small extra dose of radiation.
You can find "interesting studies" showing that homeopathy work etc... I work with MDs who expose themselves to radiation to help others. I have also worked in a radiotherapy lab in the past. I am not scared of radiation. But I know most of the related literature and the overwhelming consensus is that radiation is harmful at any dose. The idea that LNT is obsolete is a fringe position in the scientific community which almost nobody even takes seriously.
Meanwhile, a rate limited repair mechanism would imply a threshold point where the harm goes way up once above it, or if you prefer, it goes down on the low side.
This is true, but this is a highly contrived scenario. Why would a repair mechanism be rate-limited at such low doses? This is not plausible at all. A repair mechanism might get overwhelmed at high dose, but we talk about extremely lose dose. Think about it a bit more: A rate-limited repair mechanism at extremely low dose would imply that a cell hit by ionizing radiaton somehow decides not to repair a double-strand break because slightly more other cells have been hit than usual and the (body-wide?) repair limit has been reached. Why would something like this evolve? How would the body keep track of this limit? How would an individual cell even know?
Even the simplest model where there is a minimum stimulation to activate the repair mechanism which has a limited capacity would result in three different regions in a graph of exposure vs. risk. That doesn't sound at all linear to me, how about you?
This is not the simplest model. The simplest model is that there is no extra stimulation of repair mechanism at such tiny additional doses and repair is just the regular repair mechanisms (which are already very good). This is the simplest model and directly leads to LNT. Again, it is also the most plausible: Why should there be a additional repair mechanisms already at such tiny additional dose? But even the idea that extra repair is stimulated at low dose means that LNT underestimates dose, only if you assume that repair gets overwhelmed already at very small additional dose leads to the idea that LNT could overestimate dose... Again, it is not plausible at all that a tiny additional dose already overwhelms our repair mechanisms.
As for whether LNT over or under estimates the risk, that would depend on what parts of the complex curve the statistical samples came from.
Exactly, but while it is theoretically possible that non-linear effects exist, there is - so far - no clear evidence for such non-linear effect at extremely low dose. So the simplest theory which has to be preferred by Occam's razor is the linear one. And at moderate dose we know that the effect linear.