Since I managed to land my 13th weapon and glowy mount a few days ago (no FATE count, I felt it would be bad for morale), here are my $0.02.

1. I cleared it because the completion numbers for the NA servers were that bad on the unofficial census, and I am stubborn that way.
2. I suggest just getting the minions, and a small handful of weapons. If you go for completeness, expect it to take time.
3. My experience was that I would work a zone 8 FATEs before I would try the next. Any long dry spell got me traveling again. I would usually find one zone that actually would provide medals fairly steadily, and simply kept at it there.
4. Try to join FATE parties (from Party Finder or unofficial ones). Working with others takes some of the stress off.
5. On the later ones, set a goal for the number of medals for the day, and stick to it. 5 a day and then do other things, etc.