For some reason, I couldn't get my first solution to work, but I think I have
something that works.

-*[>0] +http://example.dev/current*.html +*console*

The first part prevents downloading anything greater than 0 KB. I think the
main reason it works better than -* is that it doesn't prevent the creation of
more directories. You then have to allow the html files because I think
HTTrack needs them to determine where else to look. Then of course allow
*console* because that is what you want.

The only problem with this solution is it creates lots irrelevant html files
and directories, but I think they may be necessary.

I do not understand exactly what [file] does, but for some reason it would
allow the creation of .png files and  cut the search very short.