"central oscillating machine and magnetics " -=- How does that work?
With regards to funding, there's ways and means. By deploying multiple we can increase the chances of success. That's only a short term concern, really, and one of the easiest to mitgate.
Asteroids of massive scale can be moved - applying power at the right point in time can mean so much more with regards to steering them. If the EM-Drive actually works then we can output constantly - and time wins. With regards to harvesting asteroids, these would be harvested mostly to get rid of them and remove them from orbits that pull them near Earth more than for the resources - tho in the early phases these resources might be useful, once we hit the belt between Mars and Jupiter we should have a good supply being thrown back - and once a path is cleared through that and facilities thrown out as far as the Oort, then there's more resources than we can possibly harvest - even with exponential methods(that'll need to get toned down at some point to prevent an overflow) - in hundreds of generations.
Sea platform for launch I'd not imagine to be overly stable - maybe if had enough outriggers with enough ballast a far enough distance away. I'd lean more towards some sort of baloon-suppported launch platform and seeing if can float closer to the mesosphere before applying thrust.
With hollowing out asteroids, this will only be suitable on lumps of sufficient composition/construct. If it turns out that's mostly "gravel" hollowing it out won't work to well. then even if it is a solid lump - on the inside - and assuming there's no gaseous pockets that make such a procedure unsuitable, then the act of hollowing it out presents some engineering challenges. Then you have to make sure you don't dig out too much. It might create some thermal dissipation issues too. Personally I think it makes more sense to process it and use it to build a dozen stations.