I’d expect more to come from the hemisphere around the solar apex but we’re going to be in the small number statistics regime for a long time yet. Even if interstellar objects are found annually it will be a few decades before the statistics are good enough to make a definitive statement.
I see very little chance of determining their original star. Unless they were ejected very recently from a very close neighbour the perturbations from other stars will make the trajectory very curvy. It takes a long time to travel anywhere at only 30km/s (chosen because it make the arithmetic easier — it is 0.0001c). At that speed it takes over 3 million years to travel 100 parsecs — close by in galactic terms.