It has started counting missions and I have finally completed the 5/5 melee only missions, but there seems to be no rhyme or reason why some runs counted and some didn't. I ran a wide variety of Uranus missions, including many runs on the same node under many different circumstances and it took a total of 12 missions from the first mission that counted until I finally had 5/5.
I wondered if having to enter Archwing on some missions, as you can't unequipped the Archwing weapons, was causing problems. And while none of the missions I ran where I had to submerge, regardless of if I had to use