It's been some time I used animation shop but I can tell you why this happens. .pngs, jpegs use more colours when saving a picture in comparison to a .gifs.
There is a reduced colour palate so the final animation will definitely look grainy. The more colours you have on your animation the more grainy it'll look.
Sadly there is no way to work around it. There are certain tricks that can be used to make the animation look less grainy.
One is to use colours that a similar nature to each other. For example an animation that is mostly greys. Your Avi is another example, mostly reds, browns and greys. The more colours the grainer it will look.
Another thing you could do is once you are happy with your animation you can "optimise animation" under file (I could be wrong as it's been years since I used the program).
I hope the explanation makes sense.