A/B testing is intended for testing specific, isolated details - basically the scientific method applied to user interaction / visual interface stuff, with all the meticulous attention to detail that implies. For broadly testing two completely different designs against each other, you won't get any of the benefits from it. You'll be able to find out if one design performs better than another, but you won't find out why, which is the whole point of A/B tests. This could be why you haven't found any services that do this - splits are irrelevant at that wide a scope, there are too many variables at play to pull any reasonable data from.
If you just want to find out which design works better, then instead of A/B testing, it might be easier and just as effective to just set the two designs up as independent sites (with equal marketing & stat tracking) and let nature take it's course. Or just swap one design for the other until you can see how each performs, or whatever sounds reasonable. Once you've figured that out, that's when A/B testing will start to get useful, analyzing & improving the individual, isolated elements of the design.