Well, according to my limited knowledge, ADS, Genesys, and AWR could cope with the job. Like ADS, you are able to design a multilayer PCB with the layout tool, as well as simulation can be done with the Momentum solver. However, I don't think it is much more convenient to "draw those shapes" in ADS than do it in any other PCB designing tools which have no ability to solve any EM problem. So I don't think those PCB tools, like Altium, are suitable choices even though they have a better "drawing" interface.
Maybe you can have an eye on another software named Sonnet. I heard that it is a tool facing planar EM problem which is exactly correspond to yours. And it might have a better input interface, but I'm not sure for the reason that I've never used it. And I also don't know it's price. Oh, there really exists a free version, Sonnet-lite. But I can image that your mission has already been way beyond its limits.