Don’t have any suggestions to help you collect the remaining pieces to knock out Puzzles 24-27 given your situation, however there is apparently a way to do the Community Puzzle (28) without having collected all the Chess Piece as detailed in the following post (although I have not tested this myself so I cannot personally confirm): https://www.bungie.net/en/Forum/Post/264729764/0/0 (΄◉◞౪◟◉｀)