Thanks for the reply. I ended up writing a small Python program to replace the border pixels with the color of their neighboring pixels. With a few minor tweaks, the result was excellent.
Once again, congratulations on your work!

Hi there. Excellent work. I'm using the free version and saving up to buy this pack. Do you think it would be possible to remove the black outline? I'm not asking you to do it yourself, but rather—based on your experience and knowledge—whether you think it's possible without having to retouch every single sprite. Thanks a lot for your time.