Caleb,
Here is my opinion for what it is worth within the context of owning a bottom of the line Ugartechea. First, consider this gun will never, ever be a collectible. Second, these guns are marvelous shooting guns and I can't think of a better shotgun for under $1000.
Putting those facts together, we are not limited by what is "ethical" to do to a collectible gun. That means you can do whatever makes you happy as far as beautifying the gun.
In that light, I'd probably save money and forget rebluing the boxlock and instead chemically strip it and give it a brushed coin finish.
For the stock, you can strip it yourself (protect the checkering!) and sand out some of the ugly shape in it as you go. Follow traditional oil stock refinishing methods and you'll get a great finish. You may even want to paint on some false grain as you go (people on this forum can explain how) and then oil finish over the top.
Total cost for supplies to do stock and receiver yourself? <$100.00
If the barrels need a reblue, spend it all on having a nice polish put on them AFTER you do all your refinishing so you invest as much into the barrels as is merited by the quality of your work on the rest of the gun.
Have fun with it. You can't really hurt anything and this gun will serve you well in the field for many years.
One final alternative that works remarkably well: Strip and polish all metal on the gun (and when i say polish, I mean wearing white gloves and to excellent quality) and finish it with HK black tactical paint. It sounds bizarre, but it makes for a very durable low sheen finish that is great for rainy gun work or waterfowling. I've had a $4000 beretta done this way and as crazy as paint on a double gun sounds, it actually looks pretty good. (think Beretta 686 Black Onyx for example)
