OP says he connected at LHR. That would require a single ticket. Presumably BA would not have checked his bags through to SLL had he been on separate tickets and OP would have known that at the BA check-in counter at IAD, well before departure.

OP's claim was properly filed with QR at SLL as the last delivering carrier. That has been IATA convention for 60+ years and for good reason as arranging luggage delivery at SLL is a QR, not a BA function.

Where OP seems to have misperceived things is that nobody he is talking to at BA or QR is involved in routing bags. That is handled, largely by software, and behind the scenes. The exact carrier and aircraft are non-obvious. Even if one does follow up at each lounge and gate, there really is nothing to be done here. At large airports with automated systems such as IAD, LHR, and DOH, nobody is running around looking for bags.



Once at SLL, QR contracts with a local delivery service to handle the ground delivery. Those times are almost always approximations because nobody can account for the route or traffic a taxi may encounter or whether the driver stopped for a meal.

The advice here is as almost always. Neither BA nor QR staff see anything on their monitors that the passenger can't see in WorldTracer. Repeated calls will not provide any better information, will not speed delivery, and merely serve to increase blood pressure. The sole exception here is perhaps once the bags show as arrived at the destination, e.g. SLL. At that point, one might contact local baggage services and perhaps follow up with the delivery company if one can obtain that information. If it is urgent and one is at a location where the airport is convenient, it may be easier to swing by the airport and pick up the bag.