I take a lot of panoramas, just as you describe (vertically oriented camera). I do think that they are really not quick enough to be a great substitute for an ultra-wide lens, however. I think of panos as more of a specialty, for EXTREME shots, like this:Not sure if this is useful but : I have an Oly 10 mk 2 with a 12-50 that sits on the front. If I have to get ultra wide, I will use the PANORAMA on the scene mode on the camera, take the photo with the camera on its side (usually up to 3 pictures but can do more) and stitch together with HUGIN (free software to download) which will convetr it to a TIFF and does a really good job. The focal point is at the end of the lens so I put the thumb at this point and pivot round (Thanks Rob Trek and your videos).
I do get over 9/10 panoramas that work - so this is very reliable and now just part of the armoury. May be worth a try and wont cost anything?
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I usually take many more overlapping shots than I need. I make no attempt to overlap them a certain percent - like say 1/3 - I just take a lot, gradually shifting the camera. It's faster without being too fussy about how many you take, I think. At stitching time, I often wind up using only every-other shot, but better to have too many than missing some! For stitching, I find Microsoft freeware Image Composite Editor to be just about perfect and much easier to use than Hugin:
http://research.microsoft.com/en-us/um/redmond/projects/ice/
Anyway, much fun!!