Orbital monitoring of M-type binaries is essential for constraining their fundamental properties. This is particularly useful in young systems, where the extended pre-main-sequence evolution can allow for precise isochronal dating. Here, we present the continued astrometric monitoring of the more than 200 binaries of the AstraLux Large Multiplicity Survey, building both on our previous work, archival data, and new astrometric data spanning the range of 2010-2012. The sample is very young overall --all included stars have known X-ray emission, and a significant fraction (18%) of them have recently also been identified as members of young moving groups in the solar neighborhood. We identify ~30 targets that both have indications of being young and for which an orbit either has been closed or appears possible to close in a reasonable time frame (a few years to a few decades). One of these cases, GJ 4326, is, however, identified as probably being substantially older than has been implied from its apparent moving group membership, based on astrometric and isochronal arguments. With further astrometric monitoring, these targets will provide a set of empirical isochrones, against which theoretical isochrones can be calibrated, and which can be used to evaluate the precise ages of nearby young moving groups.