If I move a unit that held a battlefield (for a point) out to base, then move another unit back into that battlefield, do I get another point?

Ruling: No, you do not get another point. You can only score each battlefield once per turn.

Nuances:

• Moving the second unit to the battlefield would not count as "conquering" it
• Triggered abilities that happen when you conquer a battlefield would not trigger in this scenario
• In order to conquer a battlefield, you have to score that battlefield, which is limited to once per turn per battlefield