Yes occasionally mine will still freeze up for no reason even after various firmware upgrades which is a pain.
I use mine paragliding, paramotoring and skydiving ( and on quadcopters, cycling and scuba...!)
Admittedly my flying ceilings are about 13k so nowt like as high as Lohan is going.
You can easily power it via the 5v usb rather than via the expensive auxiliary battery bak-pak. I use a 3s 1200 lipo and UBEC when flying paramotors. that gives me roughly 3-4 hours of additional power. As an added benefit, seeing as the 5v also goes to charge the battery it means that it warms up the camera as well via the internal lipo charging.
And while you are at it - why not take the analogue video feed out of it too - and fire it through a 5.8hgz video transmitter ?
I get about 4000 feet vertically with my quadcopter with a 600mw tx and omni directional tx, but with a high db gain antenna (since you are effectively going to be 'below' all the time directional focus shouldnt be too much of an issue) you should be able to get that up to 40k or so I'd have thought at least... for some real time video!
Anyway I hope you are going to record in 2.7k..... you know it makes sense!
Also make sure you have prores on - we want that bitrate maxed out!