WISEA J080822.18-644357.3, an M star in the Carina association, exhibits extreme infrared excess and accretion activity at an age greater than the expected accretion disk lifetime. We consider J0808 as the prototypical example of a class of M star accretion disks at ages 20 Myr, which we call "Peter Pan" disks, since they apparently refuse to grow up. We present four new Peter Pan disk candidates identified via the Disk Detective citizen science project, coupled with Gaia astrometry. We find that WISEA J044634.16-262756.1 and WISEA J094900.65-713803.1 both exhibit significant infrared excess after accounting for nearby stars within the 2MASS beams. The J0446 system has > 95% likelihood of Columba membership. The J0949 system shows > 95% likelihood of Carina membership. We present new GMOS optical spectra of all four objects, showing possible accretion signatures on all four stars. We present ground-based and TESS lightcurves of J0808 and 2MASS J0501-4337, including a large flare and aperiodic dipping activity on J0808, and strong periodicity on J0501. We find Paβ and Brγ emission indicating ongoing accretion in near-IR spectroscopy of J0808. Using observed characteristics of these systems, we discuss mechanisms that lead to accretion disks at ages 20 Myr, and find that these objects most plausibly represent long-lived CO-poor primordial disks, or "hybrid" disks, exhibiting both debris-and primordial-disk features. The question remains: why have gas-rich disks persisted so long around these particular stars?