There is the odd species of edible seaweed that flourishes in salt water, but in the end, gardening on shipboard is not really an option without considerable resources expended. Even with soybeans, I doubt the Chinese did it as frequently as is sometimes suggested, and European ships tended to have less available space. Add to that the fact that European dieticians thought of vegetables and fruit as a luxury and you can see how the concept would have a difficult start. By the time the need for veg was understood fully, ships were fast enough that fresh produce usually lasted from departure to arrival.
If you can finagle an earlier understanding of the link between fresh vegetables of some description and scurvy earlier, we might see more efforts to make it work. It'll probably still be limited to navy ships and Company Indiamen, though.
Ediut: How about the idea that scurvy is caused by absence of the 'vital principle' (it afflicts people at sea, in the desert and in winter, away from fresh plants and growing things). As a result, efforts are made to preserve the vital principle, and while it is found that young animals and fish will not help, it turns out that fresh plant shoots will. As a result, ships start carrying large amounts of chickpeas and (after Columbus) phaseoluis beamns that are periodically watered. The young shoots are eaten raw by the crew. They hate it, especially since on bean day, they have their water rations reduced, but it does them good.
It's technically about feasible given space constraints, it uses very little fres water (most of which is ingested with the plant) and it makes sense from a theoretical point of view in a way 'vitamins' or 'minerals' would not. Not exactly what we think of as gardening, though.