Personally I wouldn't use any gloss on what is going to be a finished with matte paint, this is "just in case" the two finishes don't play well.
A gentle flatting between the final paint coat and the first varnish/lacquer will help to get rid of the little bits of whatever that arrive by magic.
As to wire woolling after the final lacquer coat - only you can tell, but would be worthwhile if there are any nibs or obvious "too flat"/"too glossy" patches.