A bit of a breakthrough today: unless I change the whole driver to a synchronised boost design (i.e. with a MOSFET instead of a diode) I'm always going to be stuck with loss in the diode - to the tune of about 4-5% of the total power delivered to the LEDs, or about 0.5-0.75W, which will cause it to get pretty hot without heatsinking. It occurred to me that if I roll the diode chip over on its side, and move it toward the board edge slightly, I can pack the gap between it and the metal casing with a thermal gap filler. This makes a (not too terrible) thermal path to case in addition to the path through the PCB itself, so should help cool the diode.