I use Microsoft ICE for stitching mosaics. It seems like Microsoft no longer distributes it, so you may need to use something else.
As far as what to do with the absolute quality numbers, that is up to you. But I think it's a necessity to understand the real range. If the entire range of quality only falls by 5% from best frame to worst frame, then you are throwing away great data if you don't use most of it. If on the other hand the absolute quality falls by a third as in your case, it makes much more sense to stack fewer frames.
Your 5% and 10% stacks certainly are sharper than the 50% here, without much noticeable penalty in terms of added noise, although that may have been cleaned up some by resizing them to fit the 1600 pixel rule here; I'm not sure.
The sharpening done by Autostakkert is a simple unsharp mask. I think your latest image here is looking very sharp and is presented at a good resolution. The main problem is that you've blown out the highlights during capture; there's no way to recover from that. Other than that, I think you've got a very nice image of the south polar region.