I take that to be the equivalent of a heat sink for radiation. In my mind, thats the purpose of the black grill things on the Enterprise-A warp nacelles and the Excelsior neck. Since the Excelsior uses most of the neck for this radiation sink, it needs to devote less surface area of the nacelles to the similar function (which is why it just has that thin grill running through the length rather than the thick grills on the Ent-A.
Going back to the Warp Core, I am thinking a swirly type could work fine as the main difference between TOS Movie and TNG Era Ships are that in the TOS movies, nacelles only glow blue when going to warp. In the TNG era, they tend to glow blue continuously (for the most part). This suggests a change where the engines are being continually primed. The "pulsing" of the TNG engine room (as well as the Ent-E and Defiant Engine Rooms) match up in my mind with the continuously glowing nacelles -- it keeps them primed with minimal power consumption until they hit warp, then the pulsing gets faster.
Perhaps this is the work or refinement of transwarp drive -- initial implementation put too much wear on the components, and by keeping them continuously primed they last longer. This may also help keep radiation levels at bay, so future generation starships after the Excelsior class needed to devote less surface area to these radiation sinks.
Of course, this is all just being pulled out of my butt, so take it for a grain of salt. Unfortunately, it doesn't really fit with Voyager or the NX-01.