Sorry, I misunderstood. So both POTS lines are delivered through FIOS, ie you use 2 POTS jacks on the Verizon ONT.
I also assume that the Vonage equipment (ATA? VOIP router?) is connected to the router that Verizon provides with FIOS.

Is your setup as follows?

FIOS POTS L1 fax&meter
FIOS POTS L2 panasonic 2-line phone
VONAGE VOIP panasonic 2-line phone

According to your posts, hum appears when one of the POTS lines is hooked up to the phone but NOT when both of them are.
And there is no hum at all when using VOIP.

If that is the case (and the problem reappears) I'd call Verizon. It is possible that whatever is wrong on the their side becomes worse the more (analog) devices you add to the FIOS POTS lines. Not to say that the meter can't be defective.

BTW, you CAN use analog data devices over VOIP, but it's not worth the trouble or cost for a residential customer, imo.