At first, the army seemed the logical choice, but as I look at the reports, we seem to be doing very well offensively and defensively. As Grey Fox says the opportunity for another leader may come quickly, armies may not be a problem. The Hanging Gardens, is an opportunity given to us by the Great Library. This means there may be other nations building this high culture value Wonder already. With the Leader in PDX, which is not building a unit at the moment, and the enemy walking our territory, hurrying the Hanging Gardens there may be the way to go. PDX will be a strong builder and perhaps even our main or secondary Wonder builder in the future. Taking one turn out of its military production schedule to snatch the Gardens may be the way to go. A very potent Wonder, it makes 3 unhappy citizens content in its city and one unhappy citizen content in all friendly cities. Plus it won't expire untill the Steam Engine. To top it off, only 4 other Wonders have a higher Culture rating (well 5, but we already have the Great Library).
Edit: After checking, 4 other nations have Monarchy but no one is building the Gardens, although with all of the Great Lighthouse Wonders being built, the Gardens may be a target soon.