Hi Konrad,
A 16-bit counter running at 20 MHz overflows every 3.3 ms aprox. Are you really using switches that close for times as short as these?. I suppose they are not manually operated!. Maybe you have to test the operation of a relay?. And the time has to be measured with a high degree of precission (50 ns).
I am sure your application is very interesting. Can you tell me some words about it ?.
Thanks.

Alfredo.