I would second the above suggestion of AUS. I live here and have done the LHR-AUS flight many times, including a few in First - great way to get here. ^
It's on the 787-9 now, but one thing to bear in mind is that this service will switch to the 747 in April.
There are direct flights AUS-MSY, just last month I went there on Southwest, which was perfectly acceptable for the short hop over.
Last edited by jeffers; Jan 2, 2018 at 10:55 am
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