It should be noted that Gregory only mentions those "presbyters, deacons and other clerics" who were appointed abbots. Could it mean that the clerics where otheriwise permitted to become regular monks, and they only were expected to leave their ecclesiastical posts when elected monastic supervisors? Taking into account other letters of Gregory (see, e.g. [2357]), I would find this doubtful: monks, according to Gregory, ought not to leave their monastery for any reason, which would exclude them from any regular parrochial duties. Gregory might have assumed that the monks themselves would be disciplined in this regard by their own abbot.
It is interesting that Gregory's letter seems to suggest that these clerics became abbots without any prior monastic experience. Likely, they wanted to hold still to their old appointment in order to still receive according stipends.