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As for your question, presuming the player with Uril cast the STP you can Deflecting Swat it to Uril. That player is the owner & controller of the spell and Deflecting Swat doesn't change that.
Comprehensive Rules 112.2.
A spell’s owner is the same as the owner of the card that represents it, unless it’s a copy. In that case, the owner of the spell is the player under whose control it was put on the stack. A spell’s controller is, by default, the player who put it on the stack. Every spell has a controller.