According to the resource_tiles.json, there could be up to an average of 3 seeds per 10 plant tiles dug up. A little less than 1 seed per 5 plants harvested in that case.
If the listed drop chances are sequential and independent rather than cumulative, it could also be a 1 : 18.9 ratio which is close to your number there.
A crafting reaction to turn one plant into one (or more) seeds could be good.
That would let you maintain the farms by saving half your production to use as seed stock for the next harvest.
The main problem would then be the finite supply of water/ice.