Do not give up on NICU. It is an amazing place to work. Have you tried either calling or personally going to the unit and talk to the manager? Tell him/her that you would like to work in NICU and see if they would schedule a time to have someone show you around the unit or shadow for a few hours. This way you can see how you like it and the manager can see you in person, not just a resume.
That being said, and the following is just my opinion and might not be true, I think NICU likes to hire either people with NICU exerience or new grads. I think this is because it is specialized and different in may ways than other units.* When a nurse experienced in other areas comes in they tend to think or act like they know more and have a hard time asking for help. This makes their transition and ability to fit into the unit very hard. I have worked in several NICUs and have been told by the hiring manager that how they think a person will "fit" in among other nurses in the unit was a big factor in their decision to hire.
I say this because I wonder if you listing all your ER experience might be hurting you rather than helping. I think you should list it but maybe in a different way. ER is very different than an ICU setting but you still have valuable experiences.
Do you have experience with respiratory devices like vent, jet, oscillator, managing central lines, critical drips? Think of things you know would be similar in the NICU even if it is with adults.* Teamwork is big so highlighting that would help. What were your experiences with the babies or mothers who delivered in ER? Can you relate that to NICU? Were you involved in a case where mom delivered in ER and you were impressed by NICU team and you wanted to be a part of it? Peds patient who you were able to do teaching with patient's parents and you like that aspect of nursing? Just some thoughts.
I think it will be helpful to come across as experienced but open to learning. I hope this helps.