To answer your question directly, there are some things that an Alpha will just never do very well, if at all. Knife edge and upright snaps and spins are a few.

Moving the CG back and increasing control throws as mentioned above will help you do more with a trainer. When increasing control throws, you can go way beyond the "recommended" throws, just do it a little at a time.

Oh, if you haven't epoxied the wings together, now would be a really good time to do that. Once that's done, you won't have to worry too much about over stressing the airframe. I do inverted spins with my beater trainer all the time. Not quite enough control throws to do a snap though.

That said, I agree with much of the above, learning a lot of acrobatics is best with a more acrobatic plane. The advice to stay on the the trainer for a bit is good for the guys who want to rush on to the next thing before they are really ready for it. That doesn't sound like you in this case.