Capvermell, based on your comments over the last day or so in this thread it appears that your primary criteria when travelling LON to PMI is that you want to book relatively close to departure (it sounds like within a few weeks) while also looking for operators to not charge you a premium to do so (in the expectation they want to fill the seats any which way they can) and/or being able to redeem Avios (or any other airline currency) instead.
But I don’t think that is a hugely realistic proposition – surely the whole point of variable pricing and revenue management is to match prices more closely with demand - cheap at the start and rising as the date of travel approaches. If you want the flexibility to book late the quid pro quo for that is that it is going to be more expensive, often vastly more. (But then as an economist and statistician you will know more about that than I ever would!)
And please don’t view these comments as an attack; I’m just a little puzzled as to your expectations.