DME is not much to check i believe. you just need to check for good reception the technical precision is monitored on site i think.
after all DME just answers queries with some specified delay and the plane calculates distance from travel time minus specified delay.
just as an example a few days ago the FAA did a similar circle around DPK (Deer Park VOR near JFK).
now check the following NOTAMS with some DPK radials unusable.
(!ISP 04/136 (KJFK A2982/18) DPK NAV VOR 087-095 UNUSABLE 1804231222-1810311800
!ISP 04/135 (KJFK A2981/18) DPK NAV VOR 060-077 UNUSABLE 1804231221-1810311800
!ISP 04/134 (KJFK A2980/18) DPK NAV VOR 025-045 UNUSABLE 1804231220-1810311800)
so i would say they check both DME and VOR but the DME part is technically much more reliable i believe.
that's why for RNAV triple DME can get you good precision when you don't have GPS.
also the problem with the VOR isn't necessarily the radiating structure but reflections of the signals on certain radials resulting in errors.