On the Constellation
we do know that Hathaway
had a single, rather recessed reaction chamber located somewhere in the vicinity of the impulse engines.
I rather wonder if the warp core on a Constellation
isn't used more for high output exercises like combat or increasing warp velocities over peak transitional thresholds while a large bank of fusion generators (feeding the double bank of impulse engines) do the major lifting in terms of maintaining her cruising ability.
For example, we see in Peak Performance
somehow was taken to a remote star system with only a shred of dilithium and no remaining antimatter. She was entirely on fusion power until Boy Genius spiked it with a tiny amount of antimatter (grams of it?) to give her brief warp ability. So perhaps she can't initiate high warp without antimatter, but can sustain it once driven enough to get it to that system.