Sizing your overflow as a rectangular weir sounds like a reasonable approach. Can't say I'm familiar with the Kindsvater-Carter equation but it seems to come with some good references and it has essentially the same elements of the Francis formula that I've seen used for rectangular weirs.
Regarding API 2350, though its subject is related to "spill prevention" and it does not have info about sizing overflows, it would seem that spill prevention should be as much a part of your tank design as the overflow system.
But I'm curious, looking in the Foreword and Introduction sections of API RP 2350, it specifically states that it is not intended for crude tanks. With my experience in the chemical industry, API 2350 is referenced quite often. Anybody know any reason why the practices in API 2350 would not be useful for a crude tank or if there are other practices that are recommended for a crude tank?