By the time the 27th century arrives, famine and many diseases should have been eradicated. Its the way technology progresses. All you have to do is see how it has for us in the western world. A few hundred years ago, even the west was not safe from famine. Now it is. Soon, the third world wil also be free from famine due to technological development. New farming ideas, etc. Once a protected supply of food is found, development into the first world should occur quite fast. As a result, after Earth's population peaks, it should drop back down below 6 Billion as the result of changing familial patterns. As has happened in the west.
Of course this is discounting any major wars or disaster.
Also, why we should be knee deep in Vesuvii (or some other class of carrier). When the Kilrathi made for Earth, they wouldn't have stopped at each system destroying everything in their path. They went for the blitzkrieg style. They would reach Earth and knock it out so the command of the TC is knocked out. Therefore, other worlds would fall easier. It would give the Humans less time to muster their forces and retaliate.
Due to this, many major industrial centres, especially on the untouched far reaches of the TC, should still be operational and churning out carriers every day! Even if half of the industrial base is destroyed, thousands of ships should still be produced!
As with canon, there reaches a point where even 'canon' descriptions, such as Forstchen's, have to give way to the laws of physics and economics. These are the most canonical laws of them all!