The obvious remark is that, as Dubai returns are overnight, the F return is not necessary and you may as well come back in Club (which is what I am doing in January). You already have the miles for this. If you come back on the 747 flight then you will be able to snag seats upstairs which is almost as private as First.

Buying miles - it goes on a calendar year, so you can buy the last 5k on 1 January. This is the only way to guarantee you get the miles in your account within the next month, short of flying somewhere.

As you have a BA Amex, you could buy a fully-flexible BA ticket for at least £1,400 dated, say, next June. The 4,000+ miles will hit with your normal January miles posting. Once you have earned another 4,000 through other means (to avoid your account going into an overdraft) you can cancel the ticket and get a refund onto your credit card.

There are other promos you can do (currently 2,500 miles for 1 night in a Holiday Inn Express or higher, 5k for taking out a BA Amex, 2,515 miles for buying a £48 printer at Tesco, 10,000 miles for spending £12 on Tesco life insurance, 10k for opening a NatWest account, 2k bonus miles for doing a transfer from a hotel programme into BA Miles, 25k for opening an offshore NW account with £100k etc etc) but the miles from these activities could literally take months to post.