Are there any third-party companies that provide
a single IP address which is load-balanced over
two IP addresses owned by the end customer?
No. While it is not impossible to make something like this, for most uses its not a good solution. I have never seen any service like this.
I need to provide a solution to my customers where they
can have geographically dispersed high availability for
Is there a Pointy Haired Boss in this somewhere? Seriously, TCP geo-distribution is hard and usually best left to large companies with strong technical skills. UDP is much easier as Anycast will generally work well for stateless communication, but it's still not exactly easy.
I think the best general answer is don't do this. Or at least provide more information about the data flow, and what your most important needs are.
You could talk to some of business-to-business oriented network providers, like Level 3, Verizon et cetera. They can implement multi-site high-availability for you, on their network infrastructure. But it will be on their IP address ranges, not yours, and it won't be cheap.