I've attached a little Add-on that should do this - it does convert PNG images to JPEG if they are larger than the maximum allowed attachment filesize.

Please note that transparency will be lost in this case.
I did implement code to detect transparency and ignore the file if it does contain transparency, but that quite simply does not make much sense to me so the code to do this is commented out:
If the image filesize is larger than allowed maximum and it is not being converted to JPEG, the upload would fail.​