Noticed some odd behavior from the coin results...
I'd done several little shots, but nothing too serious - maybe 10-20 minutes at a stretch - so I'd gotten about a third of the coins at that point.
Then I did a fairly aggressive run, cleared the silver and got myself down to one gold and two copper needed.
Called it a night and did other stuff for a bit, then did another aggressive run (about 3-4 hours, 2 hours devoted to the last copper) trying to get my last three coins - cleared gold and got one copper.
My last coin was cleared after a couple of short ones, 10-15 minute runs when I first logged on or before I'd log off.
For those last few mini runs when I only had one coin left, I noticed that the coin to fish ratio had changed immensely.
Previously, I was getting two fish for every coin, an even mix of copper and silver and an average of two gold coins every ten minutes (I was buffing with my fishing hat since I was already 450 skill).
After I'd cleared the gold and silver catagories and was shooting for that last copper coin though, the ratio changed immensely - gold coins were only popping every 15 mins or so (just one per run and sometimes none), silver coins were a minority and the fish to coin ratio was well in favor of the fish, running at 80-90% fish.
This change didn't occure until around 24 hours after I'd cleared each catagory, leading me to believe that the RNG MIGHT remove certain coins from your list of possible catches and/or reduce your odds of catching them once you've cleared a catagory AND given system a chance to save.
In other words, trying to knock the quest out in big chunks might very well be counter productive - fish for an hour or so and then leave it be for a day or two and you theoretically have a better chance to catch the coins you still need since some coins will either be removed or have thier odds of being caught drastically reduced.
Since I'm sure all servers have already had thier server first achievement for this catagory knocked out, there's really no rush/hurry unless you're racing guildies/friends.
Mind you, this is 100% theory on my part, but if you only need a coin or two, then give it a rest for a bit and see what happens - worse case you've at least given your sanity a break, best case is I'm right and you finish the achievement.