You may be able to buff the nails to a shiny brass color once again, then use a browning solution to turn the nails to a bronze color. Here is a browning solution on Amazon:
Brass Darkening Solution
This stuff browns brass to a bronze color, not blacken it. A light buffing with 600 grit sandpaper or similar fine buffing may lighten the wood as well as shine the nails, but the beauty of linseed oil is that if you scratch or even re-sand the wood, a fresh coat of linseed blends everything back in flawlessly. Also, linseed oil oxides with time, and your model will darken noticeably in 5 years. I have a crossbow I made 25 years ago that was a rich red wood tone, and it darkened to a very dark red brown because of linseed oil. So your orange model won't stay orange, but darken to a burnt sienna.
A browning of the nails will be brown and blend in better with the wood. And next time make a small practice piece before trying a new technique on your beautiful hull. The problem with all the modellers using real nails in a model is that they are never subtle and stand out with too much contrast and too large in size. When you look at the Wasa hull, even with 300 years of time at the sea bottom, the nails are a subtle effect and the head so small that they practically disappear at a distance of 100m. Your hull is light orangish brown, while the real Wasa is dark walnut in color, so your nails will stand out all the more. No matter what, you can recover from almost any wrong turn given enough time and work, and I know from experience that re-work is a bitch.
Take the time to back up a few steps and make it right, or you will not be satisfied. Keep in mind what type of model you want to build, one that looks realistic as the real ship, or a model that is meant to show off the shipwrights techniques, which usually includes the nails, even when out of scale, in order to demonstrate the methods used in building the ship over the realism. I plan on copying your splines, and using my paint micro-dot technique for the nails, with the color several shades darker than whatever the wood color will be, which will probably a very dark brown on mahogany, and a darker off-white on the bottom where the white stuff is on the hull. Hang in there Doc!