Edit 2: judging on the lack of replies I start wondering if my issue is clear enough. Please tell me if I need to elaborate more.
Notice: see bottom for a co
Try using a single large BitmapData with it's own Bitmap, larger than the stage (although you might hit the limits of BitmapDatas if you have a really big stage and/or are using flash 9), and drawing new background images to it using the copyPixels method (a really fast way of copying pixels, faster than draw(), at least as far as I've seen).
Pan the large Bitmap around when you want and when you reach an edge, pan the bitmap to the other side, copyPixels the whole thing back to where it was previously (so the image should stay in the same place relative to the stage, but the Bitmap should move) and copyPixels new images where they are missing.
Since you are using alpha for the images as well, so you might want to check all the parameters of copyPixels if it doesn't copy alpha as you wanted it to (probably mergeAlpha?).
So, to recap, use a single large Bitmap that extends well over the boundaries of the stage, have the images ready as BitmapDatas, do the wrap trick and fill in the blanks with copyPixels from images.
I don't know if this way would perform better (the copyPixels over the whole bitmap worries me a little), but it's definitely something to try. Good luck :)