advisor - Should I leave out research in my NSF fellowship application if I'm not getting an LOR from the professor I worked with?

I'm pretty sure that my former advisor lied to me, manipulated me, and thinks I'm an idiot, so understandably I don't think it's a good idea to ask him for a letter of recommendation for the NSF graduate fellowship. However, my most recent academic research experience was with him, during the Spring quarter, and it's probably the most impressive research I've done, especially since he's a well known professor. I do have other research experience to talk about, but it's not quite at the same level.

But if I write about that project in my application, I imagine the committee is going to wonder why I don't have a letter of recommendation from that professor. Should I strive to minimize that research or even leave it out completely? Or is the benefit of talking about that research experience greater than the risk of being judged for not having a letter from him?

EDIT: This is why I think my advisor lied to me, manipulated me, and thinks I'm an idiot:

1) He said I couldn't work on a certain type of research project I wanted to work on because I hadn't taken a particular class. He then let two other students (undergraduates) who had not taken that class work on that type of project. One of those projects led to a publication.

2) I asked him why he let those other students work on those projects and he said it was because, while they were working on the projects, they learned stuff from that class on their own. I asked why I couldn't have also learned that stuff on my own, and he just said, "ehhhh" and refused to answer any further. [Response to comment below: those students, former classmates of mine, had not learned the material from that class on their own prior to being assigned the projects.]

3) There was only one project he said I was capable of working on. I asked if he thought it was publishable, and he said yes. I worked on it for months, and then met one of his collaborators, who said that it was not in fact publishable, but reassured me that they would post it on the internet somewhere. [Response to comment below: The collaborator didn't say this because something in the project was revealed to be less promising than they originally hoped. He said this because he viewed the piece I was working on as a small addendum to the larger project, which had already been published.]

UPDATE: In case anyone is curious, it turned out that my advisor did in fact lie to me and think I was an idiot. He did not, however, manipulate me -- that part was due to a misunderstanding.

Answer

As someone who has reviewed applications for the NSF Graduate Research Fellowship program, it would definitely be weird to see someone talk extensively about a research project and then not have the advisor write a supporting letter. It would certainly raise questions among the panelists assigned to review the application, especially if no other explanation were provided.

Normally I would not make such a suggestion, but this might be an instance where you should list the experience (if you can), but not talk about it so effusively or in great depth.