I guess I disagree with the majority here. I think there is absolutely nothing wrong with that jig, and it's perfectly well-phrased and suitable to contra dancing.
I think there are a lot of well-phrased jigs out there that we can make sound like they're not by putting an amorphous beat behind them and perhaps tying some notes over that would normally be repeated. This is one such jig. I played through it myself this morning on whistle, and I don't even think it's a particular smooth jig when you just play it normally (repeating the first note in the first bar rather than tying it over, playing the pickup triplet to the B part so that it sounds more like a pickup, and playing it at 120bpm).
I have no recommendations for how a band should use this jig other than how I think a band should play every jig-- start with four clear potatoes, use a strong beat (at least the first few times through), play so that it's phrased clearly and notes don't cross over the phrase.
To the musicians who think this jig is not well-phrased, I encourage you to play it for yourselves at 120bpm. As long as you are clear on the phrasing, the dancers will be, too. I've heard plenty of bands play jigs with a lot less clear phrasing in the melody (such as the Roaring Barmaid or Myra's) for contra dances with no problems.
-Dave