In that scenario, with lots of gene mixing going on, there isn't really a cutback of genes at any point. There is only a requirement that those thousand people are somewhere in everyone's ancestry. This is very different from them being the only ancestry. The useful gene spreads throughout the population with no bottleneck. No genetic variety goes away except in the case that it's specifically incompatible with the anti-plague gene.
Even without die-offs, you approach a situation where everyone shares all (millions) of their ancestors at some depth. Having a particular thousand somewhere in a logistically-growing list is not the same as domination.
In that scenario, with lots of gene mixing going on, there isn't really a cutback of genes at any point. There is only a requirement that those thousand people are somewhere in everyone's ancestry. This is very different from them being the only ancestry. The useful gene spreads throughout the population with no bottleneck. No genetic variety goes away except in the case that it's specifically incompatible with the anti-plague gene.
Even without die-offs, you approach a situation where everyone shares all (millions) of their ancestors at some depth. Having a particular thousand somewhere in a logistically-growing list is not the same as domination.