Why don't you use Pack and Go and create another copy of the same files. This would maintain the references.
You can also create copy of the files and rename via SOLIDWORKS explorer to maintain references.
You can also link the drawing views to new part using replace model option.
I'd suggest you try doing a Pack and Go of the original drawing, re-naming the part and drawing in the process, then make the edits to the new part. This way the new drawing should update without losing any references (but I'm not making any guarantees).
I forgot to add the parts are basically vendor parts which are pretty much dumb solids. This is one reason I just grabbed the drawing file for the one set, that was finished. Then I tried to implant the model of the other & use the copied drawing. If I were starting from scratch I'd probably just copy the files to another location, & then rename, & change the necessary model. I tried opening the drawing & then choose the replace model, but it broke the relations with the dimensions. I have another one to do so I might look at the possibilities of just starting with a model & revising it, sense it's so close to the original.
Did you try the "references" button in the open window, or get the drawing all the way open first? I admit that I haven't made drawings for unrelated import models recently (that I can remember), but this works pretty well for me when I've had to work with a file which one of my Engineers renamed before checking into the Vault, (which means the drawing can't find the new file, and is still looking for the old one). I'd say it's worth a try.
So this is under the "file/open" menu from inside SW (you bypass this screen from the "double-click to open" function).