For anyone wondering how well this might or might not actually work...
Last night I was down at my better half's sculpture studio at her university... where they have many push brooms.
I quickly strapped my phone on top of one of them with a piece of gaffer tape, and took it for a drive...
Couple of things to note...
What looks like "snow" outside is due to the fact that this was a dirty broom. This is a sculpture studio, so there was loads of white plaster dust in the broom which kicked up on rough surfaces (and the phone's LED light was on, which bounced it back). With a new clean broom that wouldn't be an issue.
Secondly, it is REALLY stable. You have to be careful with up-and-down and side-to-side motions of the handle, but that's up to the operator's skill (or lack thereof)... this was my first (and only) run.
What was surprisingly stable was the travel over different surfaces.... I went from the smooth studio floor, across a rough floor grate, onto rougher concrete outside, to pebbled concrete, to brick. It was all just about equally smooth, and smooth transitions between the surfaces... and this was just with the phone hard-strapped to the top of the broom with gaffer tape... no foam or dampening of any kind.
As Larry David would say, "Pretty, pretty, pretty, pretty good."
Fantastic Plastic Entertainment, Inc. fantasticplastic.com