If you're only using Plump Helmets, just designate a 1x1 area for seeds right next to the farm plot. Seeds go back to where they'll be needed, all good.
Designated Farmers: 15
Yeah, as soon as I read that, I knew what your problem was.
A skilled Grower (aka "farmer") will grow larger stacks of a plant than one with no/low skill. That larger stack then becomes larger meals, larger barrels of drink - it feeds into everything, a real multiplier.
Having 15 farmers means that you have none that are becoming more skilled. I feed my starting group with 1 Proficient Grower, who is the only one who harvests from word one (and thus becomes Talented/Adept that much faster), plus (later) one or two apprentices once the group grows over 40 or so. The apprentices actually HURT production at first, because half the plants suddenly are low-skill stacks and smaller, but they learn quickly and are needed for the harvesting (and I
hate to see my miners leave their jobs and walk across the map to pull up one Plump Helmet!)
Next time you start a game, include one Proficient Farmer. (Since Grower is nearly a "full time" skill, pair that with something that is not full time, like Weaponsmith or your broker/leader or Brewer - whatever works for you.)
Brew a good portion of your crops into booze to get seeds (and booze). Or Process them. You want 25 seeds* for your 5x5 farm plot. You can cook the rest.
(* Edit - NOTE - The size of a stack of plants depends on the Skill of the Grower. A stack of 4 plants will yield 4 seeds (if not cooked). A dabbling/novice Grower might produce stacks of 1, or possibly 2 - or possibly 0. A stack of 1 yields 1 seed - a stack of 0 yields... you got it. If all your farmers are no-skill, you might actually be losing seeds. Go with your best.)(I go with a spectrum of crops, and 2x2 farmplots to vary them. About 25 tiles total, but it's more management - whatever works.)
Read the Wiki - all this stuff is in there (and these are not obscure topics).