What would a space battlecruiser look like?

Would a space battlecruiser emerge as a carrier-battleship hybrid like Andromeda's Glorious Heritage class?

Yes. The Glorious Heritage class fits the carrier-battleship hybrid envisioned for a space battlecruiser.

The proposed space battlecruiser combines carrier and battleship functions. Andromeda's Glorious Heritage class is the explicit model for that hybrid.