If you get 3.5A with a full cell then the total circuit resistance must be quite high, about 350mΩ, see my DD calculator .
To get 6A you must bring it down to ~130mΩ, which will be difficult since the mosfet is already arround 60mΩ at 4V drive voltage, and a 40T is something like 12mΩ, plus spring, contact, switch, wire… etc resistance.
You can start by bridging the resistors, but that would only remove 125mΩ.