It might be possible but you certainly need a nadir and a zenith shot. I processed your handheld panorama with cubic converter to show you the "black holes" that need to be filled.
Yes, you will need a zenith shot (say at +60-65 degrees pitch), in addition to 4-around, for close to 360x180 coverage.
Screenshot below is of the nadir when shooting 4-around at -10 degrees pitch on a Canon cropped sensor body, usinha Noidal Ninja R-D3L rotator. You can see that the 'hole' at the nadir is quite small.
How did you shoot that Nadir?
I shot mine at -60-65 on NN5 in opposite direction and it is bigger than yours. Also, the view of a tripod similar to yours is visible only in SWF when played.
Can I upload it here?
I didn't shoot that pano, I don't have a Samyang FE lens myself, it was shot by 'Smooth' from panoguide.com.
I just wanted to show you that it is indeed possible to get 360x180 coverage shooting 4-around+Z+N with the Samyang FE on a Canon cropped sensor body, and I'm told the overlaps will be a little bigger with a Nikon DX cropped sensor body.
The image I posted was a screenshot when displaying the Flash VR of the pano.
The Canon APS-C cropped sensor is a different size from the Nikon DX cropped sensor. And the R-D3L rotator (excluding the leveller element) has a larger diameter footprint than the rest of the R-Dx range of rotators - 73mm for the R-D3L vs. 62mm for the R-D16/R-D8 vs. 54mm for the R-D4.
If you want a smaller nadir 'hole' just try pitching your camera/lens down a bit more for the main row. I don't know how far you can go before you find the 4-around no longer overlap with a 'zenith' shot and each other; or maybe that doesn't happen..