For that kind of application I use a lever microswitch. Most are change-over types so you can them to turn the lights on with the door open or closed by swaping one connection. The lever gives you plenty of adjustment range and minimal mechanical resistance.
If you want to do it electronically, use the magnetic switch as before but wire it to the gate of an enhancement mode MOSFET (cheap and hundreds of types to choose from) so it works to reverse the switch logic. It only needs one resistor and the MOSFET to build it:
Source pin to ground (negative supply), LED chain between the Drain pin and +12V, so it's like the MOSFET is where the magnetic switch was originally. Then wire a 100K resistor betwen the Gate pin and +12V and the magnetic switch between the Gate and ground. With the switch (and door) open the gate voltage will be pulled high by the resistor which makes the MOSFET conduct and the LED turn on. When the switch closes, the gate voltage is grounded and the switch turns off. So the switch action is effectively reversed
Brian.