I think that two things needs to be addressed: 1 that SSA requires only one chain of observers, not many and 2 that the selection of the observer has to happen only after the creation of the chain is over. Leslie explicitly wrote a lot that his Doomsday argument works only if the world is determinate.
In that case, if we play only once and the game is over and it produced only 6 observer chain, than finding that I am observer number 3 is not surprising and is an argument against that there were 100 observers.
In your example, both conditions 1 and 2 do not hold, so your model is not argument against Carter-Leslie-DA. Moreover, our Earth is a) likely not unique—there should be other habitable planets somewhere b) Its future is not determined because of quantum an chaotic effects and MWI.
However, there is one more version of DA—Universal Doomsday argument—https://arxiv.org/abs/1303.4676 It basically says that when I learn my position n, I can estimate a typical age of civilization, and thus most civilizations in the universe must be Young. As most are young, most die young. As we are typical, we also have high chance to die young.
The Universal DA is better as there is no reading from the future and it accounts the existence of many chains. It can be tested: If I ask myself my age and multiply by 2, I get approximation of typical age humans live (around 100) – and I can use it to estimate my life expectancy.
Your idea—as I understand—is that AI should not just stop self-improving but should go into war with all other possible AIs. For example, a way to stop other AIs is to attack the whole human civilization with biological viruses or start a nuclear war which damages chip production. I find it risky.