What I would recommend is getting into stage acting/performing arts. I don't know your age but if you are still in school then I would get into a drama class and learn acting. Your drama teacher will give you good feedback and point out the things that you need to work on and as an aspie. You get to read and rehearse a script over and over which fit nicely into a routine.
BTW: Don't try singing to fix this problem. Learning to tune your voice to a chromatic scale will not fix your monotone voice problems, In fact, It could make things worse.
It's important to remember that faking it is just that "faking it". No matter how hard you try. You will always come off as a fake in the eye of an NT person. But most of the time its better to fake it then to do nothing at all.