Ah, Temple's old rig! God knows my Bartech's been on that rig a few times! Glad to hear you're getting a Zephyr, should be a big upgrade for the students.
NP1s aren't exactly high capacity batteries, and likely with their age they're not going to have the kind of capacity to start everything at once, especially with the Epic being rather power-hungry (which is deceptive, because of how small the body is!). Likely rather than any protection kicking in (like sometimes happens with Dionics and other lithium-ion "smart" batteries), you're just getting a significant enough voltage drop with the startup current of the accessories that the Epic is shutting itself down, because it's no longer receiving enough voltage. The wire gauge may play into this as well - the SK doesn't have very thick wiring, not sure of the actual gauge, but it passes through a tiny little Hirose connector from the base, so it can't be much. That could certainly add to the voltage drop too.
As others have said, running an onboard battery on the EPIC makes all the sense in the world in this scenario - the setups your students are flying are generally with primes and a small mattebox, which even with a battery plate and one of your old RED bricks should still be under the 19 pounds your SK is built for. I'm a big proponent of flying the Epic with a battery on the back anyways - I think the camera is just too light to fly well without it.