I finally saw a 3-axis gimbal stabilizer, Feiyu Tech Vimble C, that had an agreeable price of $139, so I bought it. It's wonderful. It works with a smartphone or a GoPro Hero camera. There is a smartphone app you need to use to make very useful adjustments to the gimbal. The Feiyu On smartphone camera app for capturing video is so-so, but you can use any camera app to capture video. The app version for iPhone may be better. I've been using Open Camera (free) from the Play Store to capture video. If you have a second smartphone, you can use it to remotely control the panning and tilting of the gimbal mounted with the first smartphone.
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The "dead zones" can be adjusted so large movements are dampened quite a lot. Here is video comparing a smartphone camera without the gimbal to another smartphone of the same model with the gimbal (both mounted on same tripod).