Value transfer for a large number of non-contigious, filtered rows?

Basically, part of my weekly tasks is pasting a filtered range from one Excel workbook to another. Automating copy-paste on this is easy enough, but on large ranges this can take 20-30 seconds which is far too long. Value transfer is much faster, but I haven't figured out how to do it with filtered and therefore non-contigious rows. Obviously looping rows is not good since that is extremely slow as well.

What are my solutions for this?