If you arrange binary weighted loads and can remember how to count in binary, you don't need that many resistors, or switches. --the problem being its not easy to switch them in real time, without accidentally switching too many on, or turning the load off when you intend to just add a few more watts.
1k, 2k, 4K and 8 K load per phase makes 4 switches per phase for 15Kw load.
ceramics are cheap, get some arts student to fire a bucket full of them in a kiln lol. Nichrome can radiate something like 10KW per pound of wire if you let it get that hot.