Do you need accommodation and / or a car for your trip? If so you could look at booking this as a BA holiday and if the trip is more than 7 weeks in the future you only have to pay a deposit up-front, and you can pay the balance later using multiple payment methods if needed (or the same payment method but with a time gap to allow you to repay some card balance). You'll also get bonus Avios for the holiday booking on top of those from the AMEX spend.