I flew LHR-JFK-SFO-DFW-AUS and LHR-LAX-AUS both this year, and I had no problems getting all boarding passes when I checked in at LHR. One time, the agent asked if I would like to be put on a more direct routing, and since I was feeling a bit ill, I said yes. The other times, nobody said anything more than "wow - that's a lot of flights".
YMMV.