I would propose "The day of the burning Sun", or "The day of the dim Sun". Basically, either the perihelion or the apohelion could mark a periodic event defining the end of a year and the start of a new one. Your inhabitants would see the Sun going away and going back peridically, which could hold quite an interesting mythology.
The cool thing is, they'll notice that the stars aren't at the same place each of these special days. If your precession is of 30° exactly, this implies that the stars will be at the same spot relative to the day every 12 years, which could lead to a special event in your inhabitants cultures. If it is almost 30°, you can have almost a 12 years periodic event (and keeping the big party), plus a real coincidence with a previous orbit (exact same stars position) every few centuries or so (and you can throw an even greater party!).
(Of course, as @Michael Kjörling stated, life would have a hard time developing on such a planet. But let's forget that.)