Interesting. The bits I've read have said to shoot at 8-10 degrees below horizontal, so you get a smaller blank spot at the bottom. Then you can shoot 1 or 2 for the zenith to fill in the top. Do you find angling up makes for fewer gaps? Like Gary, I've been thinking of adding a few of these into my events as well, so would be good to know the quickest way to shoot them.
That's the system I use, which is based on the approved equipment for the Google Trusted Photographer scheme (of which I was once very briefly involved). Even if you shoot with the lens angled down, you'll still have the tripod to contend with, so you are creating two areas that you have to retouch/reshoot, the zenith and the nadir. Far better to shot at +7.5 degrees and just worry about the nadir. BTW, this is assuming a crop frame body.
For speed, which was the original question, four around is the best compromise between quality/speed. It does, however, create some problems with larger areas. I recently did a pano from the centre circle of Rotherham United's new ground, and because of the distance to the stands, the user couldn't really zoom into the stands very well, and pick out any great detail. For interiors, it works fine.
Some of the panorama purists might deride me for this, but I actually prefer to leave the nadir blank, and then patch it with a logo. On client tours, it's a good way of branding them with their logo, which they seem to like.
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Skyviews100 flying you out to the events would be great, but probably more expense than I can bare, but you are only an hour away, and I would be interested in spending an hour or two "fast tracking" the software next year if that is possible?
Give me a shout in the new year, and I'll see what I can do for you. Although with the investment in kit required to do pano's it might not be as expensive as you think to get somebody in. A fisheye lens, rotator head, decent tripod (if you haven't got one), stitching software and then tour software. Going to be a around a grand I reckon. Great if you have plenty of work for it.