I'm glad that someone actually brought this up. I've played this game before with no problems with this part of the game....but yeah, I'm getting the same result.
I went up against that last haystack for about 15 minutes..then I figured something was wrong. I can confirm that the haystack just jumps when hit and then continues to dodge and run around over and over again.
My rom checks out with GoodTools, and I'm using PJ1.6 w/most of the defaults. I'll try to get around to seeing if the prob comes up with 1964 or any other emulators. I suggest someone else try to do this as well.
There is a possiblility that since I haven't played this game in a while, I'm forgetting to do something, but like most of the FAQs I've come across, they just say to kill the little haystack, and then you get a cut-scene. *shrugs*