At which position should you report to ATC?
A "3-mile base" means a base to 3-mile final, with downwind being at the normal distance from the runway; it's named that because it's the base leg that moves.
All of your positions are based on the idea of a 3-mile base to (normal) final, which would mean the downwind (not base) has moved. If that's what they wanted, you would get an instruction to simply "enter right base", regardless of how far away that may start, and possibly some other reporting instruction if they're non-radar.
Also, position 1 doesn't really make sense. If you called in north or northeast of the field, they would tell you to "enter downwind", so position 1 shouldn't happen. If you were already in the pattern and they wanted you on a 3-mile final, they would tell you to "extend downwind" and either tell you 3 miles (or a landmark 3 miles away) specifically or, more likely, tell you what traffic to follow.
If you called in east or southeast of the field, tower would assume you're in position 2 or 3, not position 1, because any sensible inbound caller would have their nose pointed either at the field generally or at whichever leg of the pattern makes sense given the runway in use (i.e. wind) and their position.