I would also recommend using Revision Manager to make the changes. Here are the steps:
In the file open window, right click on the draft file and select "open with revision manager". You will see the draft file and below it, the model that drives it.
click on the draft file and then right click and select, "set action to copy". This will place a copy in the right column of revision manager. It will still have the same name, so change the name to something else like adding a "2" or "B" or whatever is your preferred revision increment.
Then go to the file menu and select "perform actions" This will create a copy of the file and the new copy will now show in the left side of revision manager where the original was listed.
If you want to change the model that drives the draft file, then right click on the model listed below the draft file and select "set action to replace" and pick a new model.
Although this sounds a little involved, it is the safest way to make copies and should avoid having detached dimensions. Using save as might lead to broken links.
Using revision manager is very powerful and can also be used to handle more complex efforts such as families of parts. You would only need to go through the detailing process once, and then using the above steps, copy that one file as many times as needed and use the replace function and you now have a bunch of detail drawings with minimal effort.
One other step you could try is to use edit links in the draft file and point to the new model but I still prefer revision manager.
Kyle