First, that's quite a model. And modeler.
Re: your challenge: Hollywood does what you want. Almost any given movie-set wood-paneled room in a mansion is styrofoam + paint.
The thing is, Hollywood set builders don't have to simulate the depth of wood. You could get a perfectly realized surface color and it would still look plastic-y unless you could give it some visual depth.
Artist's oils will provide that depth because they refract light, but you'd have to plan out the use of opaque and transparent pigments, as well as build up layers with a variety of brush techniques. The first step would be underpainting in a thinned oil paint, so it flows and settles to a smooth surface. Then you'd begin building up layers with dry-brushing and a light touch.
As an artist, I can tell you that it takes some practice to mix colors, because you need both the hue (color) and the brightness (in the art world called "value"). It seems less of a problem when using acrylic craft paints, but most of those are opaque and you end up with (literally) a plastic surface, and it looks like plastic.
For colors, you need the summer grain and the winter grain for, say, walnut or pine. Emulating poplar would be easier, since it has a fairly even color. I myself would avoid the greenish heartwood poplar streaks. Very likely, burnt umber and mixing white could get you poplar colors. Mixing white is either zinc white & whiting (powdered limestone) or zinc white & titanium white. Titanium white by itself is far too opaque, and it's really a blue color. Lead white has great depth and warmness, but it's VERY toxic and very hard to obtain... if you decide on that route, wear surgical gloves, as lead can be absorbed through the skin.
Maybe the addition of some burnt sienna would emulate cherry or fruitwood-stained poplar.
Top it all off with a substantial coat of an artist's varnish, and you might have a model that would fool the eye. Krylon/Rustoleum clear coats won't be as depth-inducing as traditional artist's varnishes, such as damar (or, from Krylon, artificial damar they call Kamar) or even white shellac with just a touch of orange shellac mixed.
Good luck! It's all do-able...