In theory, your idea of replacing one spoke at a time would probably get you in the ballpark of a straight wheel, that needed minimal tweaking to make true, but the problem is that it is impossible. To remove just one spoke, you would have to cut it and there is no way to replace it without bending the new one into an unusable state. You'll see what I mean when you start disassembling the wheel.
Doing it yourself isn't particularly difficult, but it requires some patience and $75 to $100 in tools. A decent truing stand is about $60-$70 and you'll need a decent spoke wrench. You can also use the stand to balance the wheel when you're done. Buchanan's makes a really nice wrench - a bit pricey but I'm really glad I splurged on it. As an alternative, you can ship them your hubs and rims and have them do it.
There is a decent tutorial on the forum. Also, considering the nature of your project, another skill learned would be in keeping with the goals of your build. It's a rewarding experience... "Ya, my son and I rebuilt and trued the wheels after we rebuilt the engine..."
I think I have a link to the tutorial in my first project thread.