The dowel-in-the-drill trick will work fine for making barrels. You might consider adding narrow strips of painted paper, applied with white glue, to represent the bands that hold the staves together. In those days the bands most likely would have been made of wood, rather than iron.
Does your local hobby shop have a model railroad department? If so, you might see what it has to offer in the way of "scratchbuilder's supplies." If it carries Evergreen styrene, it certainly ought to carry basswood. (The hobby shop guy may know it simply as "stripwood." Either way, it beats balsa.) The model railroaders have an enormous assortment of aftermarket parts at their disposal, some of which are useful for ship modeling too. I've found such things as cast metal grain sacks, fruit crates (some with open lids - and fruit inside), and any number of miscellaneous boxes. Most of this stuff is in HO scale (1/87), but for generic fittings like that the scale doesn't matter much.
Does the boat in the Heller kit have any detail? You can add frames, thwarts, etc. to the inside with strip styrene. To make a set of oars with a minimum of fuss, get hold of some brass wire that's about three scale inches in diameter. Heat a length of it over a candle to soften it, then mash the end in a vise. The mashed portion becomes the oar blade.
I have no idea what 1492-vintage hammocks looked like. (For that matter, I don't know whether those guys slept in hammocks - but it seems logical.) On my little model of the frigate Hancock I made the hammocks (about 200 of them are stowed in the hammock nettings, on top of the bulwarks) out of the same material I used for the furled sails: fine tissue paper painted with a mixture of PolyS paint and white glue. I'm satisfied with the results - and the hammocks look good as new more than twenty years later.
The Anatomy of the Ship book probably will give you some more ideas. As far as I'm concerned, the more of this stuff gets put on a model the more interesting it will be. Good luck.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.