Impossible scenario?

Many places build motorcycle batteries with a power inverter into a Pelican battery case. We've gotten about 3-4 hours on them in mixed standby/shooting. It might handle 80 minutes shooting to media. Element Technica makes a binary plate for IDX batteries that allows hot swap http://elementtechnica.mybigcommerce.com/technica-3d-binary-idx-dual-batter...

As far as media for the Red Epic, a 256gig card at REDCODE 8:1 @ 4K can hold 100+ minutes of media (accounting for overhead, 100 minutes is 240gigs).

The Arri Alexa should do 103 minutes with the same amount of space at ProRes444/2K. I assume its recording mechanism is a hard drive or SSD (I never rent Alexas, so excuse my ignorance there)

Hard but not impossible.

Recording:
I assume that you would like record high quality.Internal recording to SxS cards possibly would not suitable for your shoot. The newest 64gb card could record aprox. 25 min with Proress4444.And time increase when you decrease the quality.I guess lowest quality 422LT could record duration what you need, however, quality is bad.

Alexa has two card slots but you need to cut between recording to pass one card to other.Also, changing sxs while shooting will be hard.

At that point, you need to consider external recorders according to your budget and need.With using two recorders and how-swap battery changer you could use Alexa for this project.