The fact that you're getting DME distance display on both DME displays for both VOR/ILS, I would say this is not a DME issue.
From your prints, the DME indicators feed the Garmin displays.
I'm guessing this is a possible "Mode Display" issue.
If the Garmins have long range navigation, they usually display distance to the next waypoint and not VOR DME data. DME signals from the VOR's are being used, but not displayed. Crews need to know when the next turn is (next waypoint).
The crews normally will select LNAV for long range navigation. LNAV shows waypoint distance. Do the Garmins have a VOR selection for mode?