Nick, the best advice I can give you is to keep on plugging away. After I went through EC, many hospitals did not even want to look at my experience because it wasn't nursing. I had to sell myself by illustrating all of the skills I already possessed from being a paramedic and how they would translate into nursing. I also spoke to the directors or supervisors of the departments I wanted to work in or who had job openings posted. It wasn't until after my interview that they told me to just fill out the public internet form as a formality.
Especially now, in this job market, you need to do more to sell yourself. Passively filling out forms will not cut it.
Also, don't sell yourself short. Highlight those paramedic skills and assessment skills. They are worth something, make them see it.
Best of luck to you in your job search!