Suppose the IP was behind a fat enough pipe, why not load balance behind it instead of DNS load-balancing in front of it (and additionally behind each as I presume now happens)? Also, if that IP was anycast then you could ignore the issue of client latency as well, assuming you have the necessary private network behind endpoints to manage state.
If you don't like/can't solve the problem at the level of IP anycast, when not leverage a third-party anycast DNS and just have a few fixed IP for specific geographic locales, again with fat enough pipes and load balancing behind them.
I guess what I'm saying is that there's no reason for an organization, a monolithic entity, to have more that a handful IP addresses at most.