Do all you can to separate your thinking from English and instead learn how things are expressed in ASL.
I'm learning Turkish sign but unfortunately what we're being taught is more like "Signed Pidgin Turkish." (There is no Signed Exact Turkish and I'd shudder to think of trying to sign that way, it would be exhausting). So I'm trying to keep "unlearning" it as we go by talking to deaf people as much as I can.
Turkish sign (I only know a very little ASL but I suspect there are similar examples) uses facial expression for many things in place of actual "word" signs; for example, there is no discrete sign for "can/be able to." If you want to say "I didn't do it, because I couldn't do it," you would sign:
I do not, reason do not.
[raised eyebrows] [2x, with neg. frustrated expression]
You might even be able to get away with leaving out that second "not", because you've expressed the inability/frustration and negativity with your face.
You could sign somthing in pidgin but you'd have to either "talk around" it to get the real meaning (which is cumbersome) or leave out an important part of the concept (inefficient). But it really is pidgin, because it's missing half the information: remaining attached to spoken language syntax and words, you would be missing out on all those visual and spatial cues. You'd have trouble really understanding people speaking true TSL (or, I suspect, ASL as well), and become accustomed to expressing yourself fully in sign.
I have this lasting image in my mind here - 8 people sitting in a row learning the sign for "smile," and signing it with glum, deadpan faces.
And the teacher saying "what the hell was that?! Are you talking about smiling or about a funeral?"