So my shuttle blocks a ship and successfully gives it an ion token. Then the next turn I pull a red stop. Would the ship I blocked gain a second token while finishing it's movement, and then clear both? Or would it clear one and gain another?

Removing the ion token from the previous turn and adding the new one, both have the same timing window - after executing the maneuver.

The FAQ says that effects that resolve simultaneously are resolved in initiative order.

So if the player with initiative has the ion projector, the ion token is added before ion tokens are removed - so both get removed.