Deep Chandra Low Energy Transmission Grating and High Resolution Camera spectroscopic observations of the isolated neutron star candidate RX J1856.5-3754 have been analyzed to search for metallic and resonance cyclotron spectral features and for pulsation behavior. As found from earlier observations, the X-ray spectrum is well represented by an ~60 eV (7 × 10⁵ K) blackbody. No unequivocal evidence of spectral line or edge features has been found, arguing against metal-dominated models. The data contain no evidence for pulsation, and we place a 99% confidence upper limit of 2.7% on the unaccelerated pulse fraction over a wide frequency range from 10^-4 to 100 Hz. We argue that the derived interstellar medium neutral hydrogen column density of 8 × 10¹⁹ cm^-2 ≤ N_H ≤ 1.1 × 10²⁰ cm^-2 favors the larger distance from two recent Hubble Space Telescope parallax analyses, placing RX J1856.5-3754 at ~140 pc instead of ~60 pc and in the outskirts of the R CrA dark molecular cloud. That such a comparatively rare region of high interstellar matter (ISM) density is precisely where an isolated neutron star reheated by accretion of ISM would be expected is either entirely coincidental or current theoretical arguments excluding this scenario for RX J1856.5-3754 are premature. Taken at face value, the combined observational evidence—a lack of spectral and temporal features and an implied radius of R_∞ = 3.8-8.2 km that is too small for current neutron star models—points to a more compact object, such as allowed for quark matter equations of state.