①+② Given that the original couch PNG is around 205 KB and the result is only around 30KB combined you have a reduction of about 84%. So, I am not sure where you are getting the increase from but that seems to be a significant
③+④ And trying to reduce a copy of the original to 30KB using Image Alpha requires reducing it to 32 colors. In my opinion, the JPEG with the CSS mask totally wins out. As the class names stay the same you can also add new files to your texture pack later and even if texture packer repacks them into additional sheets (they are limited to 2000 square pixel) the CSS will assign the correct coordinates. Only the run to extract the alpha channel is still a manual process. The developer of Texture Packer commented to me that one can run an alpha pass from the app itself but that still requires a second export run. Texture Packer doesn't support multiple runs in on exporter.
Not sure what you are asking of me. Running custom export scripts in Texture Packer requires you to have pro. Contact the developer for an extended trial, might be possible?! I once had the chance to buy a slightly more expensive indie developer license as a one off payment, but I don't think there is currently that option. Depending on what you make a year on Banner and if the value proposition is appealing, I don't think this price matters much in the grand scheme of things.
If you don't need the "packing" you can always just use the manual approach of exporting each image manually and writing the CSS for it to get a mask. I think I posted an example of that woman somewhere and in that example I didn't use Texture Packer.
Update: There is still a lifetime tier at 99 Euros