Do not over look the discounted business class air fares that can be available with some airlines. There are restrictions which can be an issue but if you are firm on doing the cruise it can work out.
I use the AMEX for cruise charges and the AMEX points can be used for some air lines. We have used the AMEX points for two past trips on Virgin Atlantic and for TUT. VS has a miles and dollars program which can be a good option. Carol and I find the VS Upper class very acceptable business class. One draw back to VS is they do not operate from a lot of US cities. As we are in So Calif. the LAX - LHR option is a good one for us.
We have found that we need to go in a least one day before boarding if not two so doing our own air is best for us.