To make it more like a knockout,
I would make the quarter finals 4 tables with 8 players each, so that 1 player of each team is on a table, and not be drawn vs 1 other team,
just you have your table with 8 players, points are 1 - 8 and get counted together for the team once all 4 tables finished
Do I make sense??? sometimes not easy to explain in english what i mean