I remember the Widelux cameras, but I have never used one. I believe the body stays in one place while the lens sweeps. I always assumed that these pretty much had to be used on a tripod?
I did quite a few sweep panoramas with my Sony A77 which would do in camera stitching much like my current cellphone does. After much experimenting with the A77 then eventually my cell phone I found that keeping my body stiff and rotating with my legs works best for me.
Now I use a wide angle lens with several shots and stitch them together on my computer. I get much better results than with the sweep method even if I don't use a tripod.
I am not sure how you are going to keep the phone perfectly level without a tripod? Anything hand held is going to have some variance in the horizon. Using my body to stabilize the camera is the best I have been able to figure for a sweep panorama.
I used my Horzon 202 almost always handheld. The bull’s eye level is the key, it allows you to level the camera on two axes. You still have to center your subject on the right/left direction (eg, if you are in front of a building), but that is something you have to do with every image you take with any camera (unless you are taking a 360° shot).
Keeping the horizon straight is also something you have to do with almost all shots (unless of course a tilted horizon is a stylistic choice). And the up/down levelling is also something with normal shots, except of course it is very often a stylistic choice to break that levelling (with a swing lens camera breaking this results in a curved horizon, as you also get with a tilted fisheye).
The swing lens cameras not only enable a clean rotation, with the bull’s eye level (which on my Horizon is also visible in the viewfinder), you can level your camera on two axes. It is a bit strange that phones don’t show whether you are level on those two axes before you start a panoramic shot (the center line my iPhone shows during a panoramic shot appears to be linked to the up/down, but only to changes of the up/down orientation during the shot).
Your method of bracing the phone against your body appears to help significantly with the clean rotation aspect, but it cannot guarantee an up/down and “straight-horizontal” levelling (the latter might be easier if you can align the phone alongside pattern of your clothing).
Keeping a phone level during an “machine induced’ rotation is similarly difficult with a swing lens camera. You need some kind of level indicator. Of course, the built-in gyroscopes of phones and gimbals are more precise than a bull’s eye level, but since my phone doesn’t display them, I am wondering whether just adding an external fluid-based level to my phone would already help.
There is one key difference between my Horizon 202 and the panoramic modes on phones, the rotation on the faster, handholdable shutter speeds takes maybe only half a second. It is easier to keep the device level during that than during the multi-second “rotation” needed for panoramic modes on phones. There presumably is some “shutter shock” camera movement as there is with any kind of handheld camera that doesn’t have an electronic shutter start.