As someone who also speaks american, I can try to chime in-- as Leebo said its hard to give precise advice without hearing you. I also want to be clear, the usa has many different accents so keep that in mind, in case yours is very different from mine (midwest and then pacific northwest).
It is true that the Japanese R sounds like it is in between an english L and R. Personally, I think it is a little closer to english L sound than english R, but that may be subjective since it is its own unique sound.
Can you tap your R's like they do in Spanish? I will barely tap my toungue against the top of my mouth in a similar way. If I am speaking quickly it may not even touch all the way, just close enough to make the sound, for reference of how light a touch it is. At the same time I will keep my mouth in the shape of an english L sound while doing so (tongue and lips flatter, etc.) If you practice saying an english err, and the "l" like you drag out the start of little, you may notice the different mouth shapes?
I have no idea if this is how native japanese speakers make the sound, but I have never had an issue making the correct sound this way, hope it can help you :)