I think it is supposed to run way forward.
When reassembling my 61 speedster with a new chain, it had to be WAY in the front or almost all the way in the back, anything else would have required a half link, and I doubt Schwinn did that.
There were marks on the dropout where the axle had been way forward like that at some point in the bike's life.
Of the two possible positions, I chose the way forward one because it allows for chain stretch. I suspect the factory did the same.
I know none of that matters with a derailleur like you have, but it seems likely since the frame, fender, and fender support design is the same (or mostly so), Schwinn would have put the wheel in about the same spot. As you noted, the fender fits worse the farther back you go.
This pic doesn't show it that well, but the axle is at the extreme front of the slot. Maybe you can zoom in.