Thank you everyone for your quick responses, your responses are incredibly helpful. Would you mind commenting on some follow up questions that arose:

When you talk about the "gateway being changed", are you suggesting that if one of the DUB sectors got cancelled I could request that this particular flight is taken out of the itinerary completely and I start/end the trip in LHR, or how could the 300 miles gateway be applied in practice, as it's not something that I am familiar with?

Could I move the DUB-LHR flight forward / LHR-DUB backward a few days so not to have them at the front/end of the trip? So in this case the order stays as is (start in DUB and end in DUB), but I don't need to do the turnarounds at the beginning and end of the trip, so I'd do it as 3 trips. LHR-DUB-LHR one day, then then LHR-USA TP run and then, a few days/weeks later, do the last segment of the trip to fly LHR-DUB-LHR - of course it also makes the luggage issue for the long haul trip much easier.
If this is possible, does one/both of those DUB flights need to be cancelled to do this, or could this be done through a cancellation of any of the other segments in the trip? I know that BA let's you move both segments in a 'standard return flight itinerary' even if only one of the flights got cancelled, but does this keep applying for itineraries with more than 2 segments and flights operated not by BA (but on a BA codeshare)?

Is there any more information that you'd need to help answer this?