Likely it will be necessary to use multiple fixed cameras with 360 coverage and stitching/anti-spin in software
Since this is basically my current field of work (not for rockets, unfortunately), I'd say that your best bet is to leave the production of the final images/videos (the stitching/movement correction part) to a computer on the ground. Just hang some cameras on there that are as dumb (and light) as possible. What I wonder, though, is your planned means of delivery... You definitely don't want to clog up your telemetry stream with video...