I see, your proposed argument isn't directly analogous to the standard Doomsday Argument, but more like a (hypothetical) variant that gives a number of non-anthropic reasons for expecting doom in the near future, and also says "BTW, a near future doom would explain why we have low birth rank."

I'm not sure that such anthropic explanations make sense, but if you're not mainly depending on anthropic reasoning to make your case, then the counterarguments aren't so important.

BTW, I agree it is likely that alien civilizations would expand at near the speed of light, but not necessarily to finish some computation as quickly as possible. (Once you're immortal, it's not clear why speed matters.) Another reason is that because the universe itself is expanding, the slower those civilizations expand, the less mass/energy they will eventually have access to.