Well, my first suggestion is (at least in the case of the smaller, upper masts, such as the topgallant and royal masts) to get rid of the plastic pieces and replace them with wood. Styrene is a wonderful material for many purposes, but not a good one for spars. It's too flexible. In the case of a big, fat lower mast the difference is negligible, but in an upper mast or yard wood is far easier to rig.
Upper masts usually are pretty simple in configuration; there usually aren't any mast bands, hounds, etc. If you aren't set up to turn spars on a lathe you can do it quite effectively with an electric drill and a piece of sandpaper. If you don't have access to any of the unusual woods I mentioned earlier, a local dealer may have some dowel stock that will work perfectly well. Places like Lowe's and hobby shops seem to be stocking dowels in two materials these days: oak and birch. Oak is lousy for ship models because the grain is too course, but birch works really nicely. Just be sure to pick a dowel whose grain is nice, straight, and parallel to the length. If the grain crosses the dowel it will warp eventuallly.
If you do want to imitate wood with plastic, it can in fact be done pretty convincingly. Start out by painting the spar with a yellowish tan color, and let it dry thoroughly. Then pick a darker, reddish-brown paint and put a thick dollop of it, from the bottom of the jar, on a piece of paper. To apply it to the mast, use the extremity of the Mk.1mod3 index finger. Dip your finger in the paint, wipe most of it off on your cat or some other convenient repository, and wipe the remainder lengthwise along the spar. If too much of the dark color is deposited, use another finger to wipe most of it off. To get really sophisticated, pick yet a third wood-like color and repeat the process. If you're careful (and willing to make several tries), the illusion of wood grain will be really effective.
This trick works with virtually any kind of hobby paint. One of the byproducts of the current boom in aircraft and armor modeling is the huge range of browns, beiges, yellow ochres, and so forth that can be found on the Testors and Polly-Scale racks. (Polly-Scale is my favorite, but I'm sure the others will work.) Ignore the labels like "Italian Desert Sand" and "Panzer Red-Brown"; squint a little at the paint bottles and pick out the ones that look like wood.
Good luck. Hope this helps.