Is there a way to convert automatically uploaded PNGs to JPEGs and keep the original? In other words, let the user upload a PNG, but show in wordpress (thumbnails, large, medium, etc) the JPEG version and only show the original uploaded PNG when Wordpress request the full image.
There is a way, I recommend you combine the imagefx plugin with a custom function , http://wordpress.org/extend/plugins/imagefx/
You can read about it here: http://ottopress.com/tag/gd/ , and use a function like one found here: http://stackoverflow.com/questions/1201798/use-php-to-convert-png-to-jpg-with-compression
It would look something like (not tested):
But remember they are not the same format and .jpg does doesn't support alpha-transparency