i did a bit of scrolling about the map and found Liaedin, it's under 30LY away but i don't think my eagle can get there. at least it didn't show as routable for me, but then i've found with a bit of juggling i can get unroutable systems to show up as routable by forcing it to think of different systems near by. i flew out in a sidewinder and traded in for a viper.
no reason why you couldnt sell the eagle (sell modules first, then ship), fly out in a sidey then buy the eagle back. it will cost a bit, but unless your balance is struggling to fit in the insurance cost it should be quite affordable.
one problem with the short jump range will be when you need to do the rank up missions. they might ask you to find combat stabalisers or personal weapons. both are a trek and both will involve smuggling them back into station, but the combat stabs are freaking miles away! so you'd need another ship for that, sidey, hauler or adder would all be good candidates depending on your funds. the eagle and the viper are pure combat ships and are not built for long distance flying, so where ever you go chances are a second ship will be needed. doing the combat stab run is where i found out about the routable issues. i could get there just fine (with my weight set to include the goods for the return trip to ensure i didnt strand myself!). yet on the return trip it would not route home without some juggling.
not sure if it's worth flying even further to get to a cluster of empire systems. i stayed near 3447 as all my friends are in the area. were i flying solo i think i might be tempted to haul myself all the way to the main empire, not this tiny outpost in the middle of fed space.
on the plus side the first station is under 400Ls from the drop in star, and there are 2 more stations over 1K Ls away should you want to check different bullitin boards. there is also a high tech fed system just below it with all the class A modules you can shake a stick at, though it is 2.6K Ls from drop in.