Welcome to Flyertalk, welcome to the BA forum, it's good to see you here offBia. And I very much hope you can continue to participate here.

Personally - and this is on the basis that I had to go to NYC somehow or other - is to book a CW or WTP redemption ticket (or indeed via AA, IB, AB, EI etc). This ticket is essentially flexible until 24 hours before departure, it can be cancelled or changed up to that point, though there are some change or redeposit charges. Then I would check BA.com once a day, in the UK morning, to see if a redemption came up. It is the case that more availability comes on stream in the final three days before departure, so if your trip is entirely discretionary then you could just leave it until then.

The bucket for UuA and redemptions is the same, so there isn't any point getting a revenue ticket in the circumstances you describe. However you are more likely to get a cash upgrade offer (POUG) on a revenue ticket than a redemption ticket. Both types allow for airport upgrades (AUPs). Thread in the Dashboard give the details of this.