Strategy is courtesy Rat_Farts, who mailed it around. So apparently, Galadriel’s Gift appears to be less RNG than expected, and patterns emerge in consecutive results.

Strategy to obtain your second city deed is as follows (though, if this works, you could use it for any item you want): Collect a fairly large number of Tokens, so you can play the game a large number of times in a row (see also here). Now when playing the riddles, look closely at the position of the deed in each result. According to some, there is likely to be a pattern that emerges which makes you able to correctly guess where the deed will go next game around 50% of the time.

I have no clue if this works, but if someone is successful in this, please let me know in the comments!