Hmmm Sky...
We are talking here about a spherical panorama, in which you can look all the way around and up and down.
For your set up, I would suggest portrait orientation of camera.
Try to organise so that the nadir (south pole) is in shot in the bottom of the frame. I suspect that will be possible with the GoPro.
Shoot so that you have 30% overlap in your images... more is not a problem, you can either edit or let PTgui sort it for you.
PTgui is an excellent stitcher and better than anything else I've tried, although there is a bit of a learning curve, thing to do is to take it a bit at a time.
I've suggested how to set up in a post above. The result of that stitch will give you a 360 x 180˙ equi-rectangular flat image, with the bottom half inhabited by your 'downwards' pointing panorama, and an area of probably black above, where the horizon finishes and the sky should continue to as a vault to the zenith (north pole of the panorama)
For the sky... Now is the time to find some sky shots and make 'top half' panoramas... some panorama shooters collect skys that they can drop in at the time of post production, and this is what you need. You have a machine above you to be got rid of.
So export the panorama from PTGui as an equi-rectangular tif at full resolution, and open in photoshop. Then it is time to extract the area above the panorama and drop in a sky... having done that re-import the image to PTGui and wrap into a ball, or, better, I use Pano2VR. Both excellent programs and mac!
If you want to send me a set of images I'll wrap 'em for you.
Best
Hugh