Context. Millisecond pulsars (MSPs) represent nearly half of the more than 160 currently known γ-ray pulsars detected by the Large Area Telescope on the Fermi satellite, and a third of all known MSPs are seen in γ rays. The least energetic γ-ray MSPs enable us to probe the so-called deathline for high-energy emission, i.e., the spin-down luminosity limit under which pulsars (PSRs) cease to produce detectable high-energy radiation. Characterizing the MSP luminosity distribution helps to determine their contribution to the Galactic diffuse γ-ray emission. Aims. Because of the Shklovskii effect, precise proper motion and distance measurements are key ingredients for determining the spin-down luminosities of MSPs accurately. Our aim is to obtain new measurements of these parameters for γ-ray MSPs when possible, and clarify the relationship between the γ-ray luminosity of pulsars and their spin-down luminosity. Detecting low spin-down luminosity pulsars in γ rays and characterizing their spin properties is also particularly interesting for constraining the deathline for high-energy emission. Methods. We made use of the high-quality pulsar timing data recorded at the Nançay Radio Telescope over several years to characterize the properties of a selection of MSPs. For one of the pulsars, the dataset was complemented with Westerbork Synthesis Radio Telescope observations. The rotation ephemerides derived from this analysis were also used to search the LAT data for new γ-ray MSPs. Results. For the MSPs considered in this study, we obtained new transverse proper motion measurements or updated the existing ones, and placed new distance constraints for some of them, with four new timing parallax measurements. We discovered significant GeV γ-ray signals from four MSPs, i.e., PSRs J0740+6620, J0931−1902, J1455−3330, and J1730−2304. The latter is now the least energetic γ-ray pulsar found to date. Despite the improved ˙ E and L γ estimates, the relationship between these two quantities remains unclear, especially at low ˙ E values.Read less <