If you believe the DA, and you also believe you're being simulated (with some probability), then you should believe to be among the last N% humans in the simulation. So you don't escape the DA entirely.
However, it may be that if you believe yourself to be likely in a simulation, you shouldn't believe the DA at all. The DA assumes you know how many humans lived before you, and that you're not special among them. Both may be false in a simulation of human history: it may not have simulated all the humans and pre-humans who ever lived, and/or you may be in a special subset of humans being simulated with extra fidelity. Not to mention that only periods of your life may be simulated, possibly out of order or without causal structure.
I'm not talking about the DA only, I'm talking about the assumption that our experiences should be more-or-less ordinary. And this is designed to escape the DA; it's the only reason to think you are simulated in the first place.
Really, I got the whole idea from HPMOR: fulfilling a scary prophecy on your own terms.
A self-modifying AI is built to serve humanity. The builders know, of course, that this is much riskier than it seems, because its success would render their own observations extremely rare. To solve the problem, they direct the AI to create billions of simulated humanities in the hope that this will serve as a Schelling point to them, and make their own universe almost certainly simulated.
Plausible?