You are trying to predict the length of the sequence of all humans, so you have no way to know whether or not you are ‘early in the sequence’. You can’t use the number you are trying to predict as an input to your prediction.
The tank problem doesn’t tell you how many tanks Germany will go on to build - it just tells you how many they have already built.
‘Good news! The war is almost over! The chances are these tank serial numbers all fall among the last 95% of the tanks Germany will ever produce!’
The difference is that the german tank sample can only be drawn from the pool of existing tanks so far. But when you consider your own birth, that's a sample out of the pool of all the humans, including future ones. Because future humans can also ponder their own place in the sequence, and where they find themselves is distributed uniformly over the sequence of all humans.
To apply the doomsday argument to tanks, we need to fix the sampling. It won't work for allies grabbing german tank samples. We have to think from the point of view of the tank; say a copy of your consciousness is being uploaded to an army of tanks. If you wake up as tank #734, could there eventually be millions of tanks? Maybe so, but there's only a 5% chance that you are one of the first 5% tanks, so there's a very good chance that there will be less than 734*20 tanks in total.
The tank problem doesn’t tell you how many tanks Germany will go on to build - it just tells you how many they have already built.
‘Good news! The war is almost over! The chances are these tank serial numbers all fall among the last 95% of the tanks Germany will ever produce!’