The Great Attractor Fleet
Faster-than-light travel is achieved by "translating" a ship into hyperspace. Like normal space, hyperspace is mostly empty. The topography of hyperspace is based on the energy potentials of that dimension. Think of these potentials as mountains and valleys, hills and passes, strongly influenced by objects in normal space. Small, light ships can push themselves out of the valleys, to higher energy potentials, reaching places that heavier ships can't get to. Heavier ships must travel the slower, well-established routes through the lower energy potential valleys.
If a ship is heavy enough, it can't translate into hyperspace at all. One of the hazards of hyperspatial travel is Corrado Runaway, where a ship acquires additional mass, taking it over the limit. That ship can't return to normal space and is doomed. There is a strict upper mass limit. (This is, of course, the situation in Collision Imminent!)
The ships of the Great Attractor Fleet use cutting-edge hyperspatial technology, the best known in the Milky Way, from the greatest physicists in the Galaxy. There aren't any short-cuts. Ten light years a day is the top possible speed for the duration of the Expedition. Yes, this is very slow, at 0.42 light-years/hour, which makes it interesting. Earth to Alpha Centauri is a neighborhood trip, less than ten hours to make. It takes several years to get from the Rim of the Galaxy to the Core. Crossing the voids between galaxies takes centuries — nearly 700 years between the Milky Way and Andromeda. Space is very, very, very big.
Now consider the starships at the amazing Starship Dimensions site. If you click on the -100x tab, you'll see V'ger and the Whale Probe from Star Trek. These will not fit in this version of hyperspace. Scrolling down, Babylon Five (and most O'Neill types of space habitats) are also too big. The Death Star is not possible in this Universe, where it would be limited to relativistic velocities under the speed of light.
Most of the larger ships on the -10x tab are also too big, such as the Borg Cube, the Stanford Torus, and the Bernal Sphere. The Deep Space Nine station is at the upper end of hyperspace feasible for this Universe. Every ship but the first on the -2x tab are hyperspace-capable.
Thus the Great Attractor Fleet is more like the convoy from Battlestar Galactica, although one that planned for the journey. The Fleet is also larger, with more than a thousand ships, from the tiny Deep Dark, to science ships comparable to the Enterprise-D, to the fleet ships of the Doctors Across the Galaxy planetary emergency rescue and teaching hospitals. (One DAtG ship alone is a planet-saving miracle of medical talent. To have several in the Fleet is unprecedented.) There are ships from scores of different peoples, breathing different atmospheres, eating different foods, tolerating different radiations, all intent on exploration.
What are their stories? Who will join them on the way? Who will leave?