Considering the average distance between stars in the galaxy is about 5 light years, the 15 LY jump range on the Aquilla wouldn't be that crippling it you were planning on stopping at all the systems anyway. It would mostly affect the trip back home after the mission.
Arrange the mission route so the stars on the way back have to be mapped too. You'd have one route headed out stopping at stars as close to 15 ly apart but still heading outward, do a bunch of surveys out past some distance, then on the return trip you'd map other stars that are as close to 15 ly apart, but still on the way back.
This way you'd have plenty of locations still to survey on both the outbound and inbound legs of the mission, while doing most of your science beyond some limit. Since it is a 5 year mission, each leg could be 1 year long, and assuming only 10 ly travel per week (due to having to angle back and forth from star to star), you'd explore 50 systems on the way out, wind up 500 ly out at the end of the first year, explore a bunch of systems/oddities in one area for 3 years, then spend the last year heading back and mapping another 50 systems. This is assuming you only spend 1 week per system on the legs, just mapping habitable zones and marking planetary orbits for follow-on teams.
