ASF The file cannot be opened because of header error - VLC, Media Player, free editors can open

As described in the subject, I have a ton of very old ASF files that I would like to edit in Premiere. VLC, Media Player, and even free editors can read these files but Premiere throws the error "The file cannot be opened because of a header error" on import. As a work-around I can pass these files through a converter but it would take a while and I'd rather not suffer a generation loss through recompression. Is there any way to make Premiere read these files and if not, is there a good program/format to get lossless conversion?
Experience level: beginner.