Yes, you have to roast the meat and vegetables first, but you barely have to wash them, the carrots don't need to be peeled, the onions really don't either, and I turned my back on celery last year and haven't missed it. And everything roasts while you are out of the room, doing something more fun, like riding the bike trainer. Then it all goes into the pot or slow cooker, add your water, and again, you leave the room. I sometimes leave the house, even if it is on the stove, but then I don't leave the dogs in the house. If you are going to leave the house for the whole day, use the slow cooker. When it is done, you can lift the larger pieces out with a slotted spoon, so by the time you tip it into the colander, there aren't so many large pieces to splash all over. (psst- Apron) Set the colander over a bowl with a spout and handle. I eschew the whole cool and skim fat step. If it is really important to you to get rid of the fat, you can do that after it is frozen. Pour it into containers and freeze. Also, I don't obsess over every last drop. If there are a few tablespoons leftover, I give them to the dog.
There are a couple of things that are unclear. If you are using a copper pot heavy enough to break your wrists, how are you ending up with 2 cups of broth? I put a carcass, left over from roast chicken, in a 2 qt pot, scrape everything else out of the roasting pan--browned bits, onions, herbs--cover with water, cover and simmer for 4-6 hours and I end up with 2-3 cups of broth. One carcass. Although I have saved all the bones.
I think you could try a few alternatives. If you want to use the heavy pot and make a lot, use Mom's recipe with the three whole chickens that go in raw with your veg and simmer away. You can remove the breast meat after an hour and use it for something else. This is a production, but you should end up with several quarts of stock. It is a Contessa recipe, but still pretty good.
Or you could do the slow cooker method. If you make the slow cooker beef broth one time, I don't think you would ever go back to canned.
Also too? The broth is not masked in the stew, it makes the stew. It elevates it from Whitman Sampler to Maison du Chocolate. I actually think the final stew is so much better than just the broth alone. I'm never tempted to drink the broth. But the dogs think I should rub it on my body.