They actually haven't run out of canon material. There is a lot more out there than you think, spread across PS2 games, DS versions, and manga. Since all of the story is set in parallel repeats of the summer in 1983, or the events leading up to that time, all of it is canon.
For instance, the cursed magatama of love episode on the Rei OVAs was based on the PS2 third person shooter doujin game Higurashi Daybreak, originally released in 2006. For the DS games, there are arcs about Rena's past, ones about Hanyuu's past, another from a female policewoman's perspective, and so on.