A possible explanation of this appears on the Subach HL-7. It's an X-Ray laser (Xaser) that is in full deployment by the time FS2 starts, but it's stated in the tech room that they knew how to make such a weapon at the time of the T-V war - it was just too expensive to justify since Vasudans didn't have shields. So, that's at least one example of Terran scientists knowing how to make advanced tech but not needing it until the Shivans came around. The Banshee could have been another such weapon rushed to the frontlines in a prototype state, much like the Prometheus was (it's even stated to be a prototype in the FS1 Tech Room).
This also allows for some quick design of ships, such as the Ulysses. It's obviously a Vasudan frame, and the most likely explanation for the "joint" aspect of the project is that the Vasudans were working on a next-generation Space Superiority fighter to counter the Apollo at the time of the Shivan invasion, and then shared that project with the Terrans so they could put the Prometheus on it and fit a Terran cockpit.
So, it's possible that nothing was designed in "three weeks", and the time that the games takes place was just a coincidence of advanced scientific knowledge and good timing of the R&D of both sides trying to end a stalemate war.
Now, FS2 throws a curveball at this theory in the form of the Pegasus stealth fighter and the AWACS specifically designed to use in the nebula, but there are holes in that statement. The Charybdis-class ships are never stated to be cutting edge, newly-developed technology, simply the "latest" sensor package available. And fitting in with the good timing of R&D from FS1, the Pegasus fighter could have been in development for years, and Commander Vincey's line that it was "developed for allied operations in the nebula" could have just been an oversight of the script writers for the game. It could also be that the Pegasus was quickly redesigned in some unknown way to operate better in the nebula.
My point is, we don't have the whole story about how long ships have been in development, and the game designers probably didn't either. It's open to interpretation.