If I'm defending with a single unit and the opponent moves into the battlefield to start a showdown, can I play Arcane Shift, banish my unit and play it back to the same showdown given that I technically still have control?

Yes, you can do this. Because you are in a showdown, you maintain control of the battlefield throughout the entire process, even if your unit is temporarily banished.

According to the official FAQ regarding this interaction:

Ruling: You maintain control of the battlefield during the showdown and can replay the unit to that battlefield. The player who controls a battlefield at the beginning of a showdown maintains control until the showdown is completed, even if they temporarily have no units there.

Sequence of Events:

1. Opponent attacks: Your solo defender is at the battlefield.
2. Showdown begins: You are the defender.
3. Play Arcane Shift: You play the spell as an [Action] during the showdown.
4. Banishment: Your defender is banished. Because you are in a showdown, the battlefield remains under your control (it is "contested").
5. Replay: You play the unit back to the same battlefield for free.
6. Combat continues: The showdown proceeds, and your replayed unit participates as a defender.

Important Nuances:

• Contested Status: This only works because you are in a showdown. If you were not in a showdown (e.g., during your own turn), you would lose control of the battlefield the moment your only unit left, preventing you from playing it back to that location.
• New Game Object: When you banish and replay the unit, it is treated as a new game object. If that unit has a "When I Defend" ability, it will trigger again when it re-enters the battlefield as a defender.
• Targeting: Remember that Arcane Shift requires targeting both a friendly unit and an enemy unit at the battlefield to be played. You cannot play it if there is no enemy unit present.