Really it was a time issue. Even if you assume the hobbits of the Shire had both the technological capacity to create a functional guided rocket and the industrial capacity to manufacture it ready to go, it takes around about a decade to bring a rocket development program from conception through to completion, even optimistically. Factor in the fact that there’s a single unique and irreplaceable payload and if you fail to hit the target you’ve basically delivered the ring to Sauron, given it’s apparent indestructibility, the reliability requirements would push the development time back a lot. It might take 20 or 30 years for the rocket to truly be ready for that mission. They were only able to confirm that what they’ve found actually is the one ring less than a couple years from when Sauron would have invaded everyone, so even with the most optimistic possible appraisal of the military industrial complex of the free peoples of Middle Earth there simply wasn’t time. It’s one of those projects where throwing more bodies at it just slows things down.