Beam-helicity and beam-charge asymmetries in the hard exclusive leptoproduction of real photons from an unpolarised hydrogen target by a 27.6 GeV lepton beam are extracted from the HERMES data set of 2006-2007 using a missing-mass event selection technique. The asymmetry amplitudes extracted from this data set are more precise than those extracted from the earlier data set of 1996-2005 previously analysed in the same manner by HERMES. The results from the two data sets are compatible with each other. Results from these combined data sets are extracted and constitute the most precise asymmetry amplitude measurements made in the HERMES kinematic region using a missing-mass event selection technique.