One solution to go for when stabilizing long takes from drones or car-mounted cameras is 3D stabilization.
You need a 3D tracker of course and if you use Syntheyes you could even do the whole thing in that software.
But you can also do the stabilization in Fusion by importing the 3D camera track. The whole process is similar to
I once did: You project from your shaky camera track and re-capture it using a smoothed camera path.
The fuse that Marek has mentioned can be found
here. The docs used to be on vfxpedia but there's a video on my blog that explains its usage. It's basically a Mercalli-like proof of concept that I have never tried on forward-moving footage. If it works for your helicopter shot let me know
creating motion vectors in 6K would be a massive task but my Fuse reduces any motion vectors to a really small array (like 4x4) anyways so you could create the vectors using a really small proxy version of your footage and then multiply their values accordingly.