But they would need something a lot more aerodynamic than a big box to fly in a slipstream tunnel!
No, they wouldn't. You're completely misunderstanding the principle, perhaps because you're taking the name "slipstream" too literally. Quantum slipstream ships need to be relatively narrow, but beyond that, the specifics of shape are irrelevant. Something shaped like a log would work just as well as something shaped like a dart, as long as they were both narrow enough to fit in the conduit.
Not even the Sovereign-class ships, even with their oblong saucers and sleek engineering sections, have slip-stream capabilities.
That's not about "aerodynamics," it's simply about how wide the ship is
. A wider ship would need a wider slipstream conduit to get through, and the wider the conduit, the more power it takes and the harder it is to stabilize. You were on the right track when you talked in terms of going through a tunnel. It's purely a matter of clearance.
More importantly, it's about the novel editors not wanting the E-E to be slipstream-equipped at this point. The rest is just a handwave to justify that decision.