This construction was, presumably, developed for translating an Ancient Chinese expression. I don't know how wide this expression or similar ones are used in AC, but 淮南子 uses 居一年 just as it is used in Japanese today (to be exact, Japanese used this as a material for its own new construction).
居一年,胡人大入塞
The traditional
kambun style translates this into:
居ること一年、胡人大いに塞に入る。
Again, I don't know if other Chinese verbs can take a quantifier object and make an independent clause. Nor am I to suggest 淮南子 is the direct source of this Japanese construction. Having said that, the Japanese construction seems to be used with a variety of verbs. Two more examples than have been mentioned are:
今を遡ること87年、私たちの祖先はこの大陸に新たな国家を建設した。
歩くこと2時間、登山家たちは山頂に到着した。