It's totally random, unfortunately.
I saved up a bunch of points when I was getting all the trophies and saved before redeeming the points then shut the game off before it auto saved to get a bunch of the fish prints.
I had the same problem with Bug Off. Flick kept giving me duplicates of everything except for the one item I actually wanted duplicates of - the Spiderweb. I didn't really want any of the other items again
I could be in the minority here, but I kinda wish they just cycled through the sets so I can at least get a few that way.
I had no idea it was random. I did one of the tourneys last year and I kept getting new items each time, except for maybe once. That's really annoying. Sorry.
Oh I spent a looong time yesterday trying to get more fish drying racks too, but kept getting the fish ponchette and the tackle bag over and over and over again, I just dumped them all in the trash, I did eventually end up getting 2 fish drying racks but I had originally set out to get at least 8. I'll just trade for them in future. Same with the Bug Off, I'm not going through all that when I need about 20 Spider Webs.