5x4 10 inch drums

WHY do you want to keep your stock brakes?? As you can already tell, replacement drums are next to impossible to find, and if you do, you're going to pay a premium price for them. Plus the fact that if you ever need to replace a drum, it'll have to get machined again, too.
If he's "making you an axle", just use his standard 5x4.5 axles instead, and use the readily available 5x4.5 10 or 11 inch drums and backing plates, and you'll probably be money ahead, especially in the long run. No machining, no drilling. And you'll be able to get replacement parts cheaply.