Never used the Contour but does the roam use the same helmet mount? If so, and 1080 good enough then it would seem suitable.
The Insta360 is bulkier and more awkward to mount. The image stabilistion is internal software processing and nothing to do with cutting an area of the 360 footage. The dual lens (ie 360 rather than wideangle lens which is single direction) isn't really going to work unless you mount it on a stick on top of the helmet...clearly not an option for caving. Closely mounted it would give you some options of forward + backward video views which could be useful for creativity. Insta do some intersting kit and I use them for 360 photography in buildings when I don't need true pixelpeeping definition. Basic battery life is shockingly poor in 360 versions.
I use gopro (or far cheaper clones) for convenience of their now common finger mount. Mounts each side allow a spare torch to be fitted.
Note that the newest gopros are water-resitant but now larger body (9 and 10). They do have amazing image stabilisation (a touch better than Insta again.... for now).
May be worth looking at what type of cameras are used by people who do motorcycle goontube stuff as they'd have a requirement for helmet mounts, water-resistance and general robustness possibly. Surprisingly, perhaps, I know a lot of motorcylists (who video for themselves not goontube) who use old Hero4 gopros in the waterproof casing still. The old Drift Ghost is also popular but I'm not familiar with the newer versions of those and no nothing about battery life.