Ah! I think I figured it out! I kept experimenting and I came up with this:
<<list-links "[tag{!!title}] -[tag[status]tagging[]]">>
Looks like it's working by doing 2 runs, the first to get everything tagged by the current tiddler then removing the results of another run that gets everything tagged with a status tag. I'm not sure if there is a more efficient way, but I guess this works for now!