Hi Milan,
Maybe i did not understand You post, but ...
Use Timer 2 only for display,keyboard(debouncing) and maybe for incrementing some timeout variables.
Timer 0 is enough to measure capacitor.
I'm not sure why You plane simultaneously charging from more than one source transistor Q5..Q9.
You start measuring first trough strongest source Q5 .
If You
-A) do not receive Ready0 flag in 1..2 seconds
- a) If P3.2 is HIGH - You have too big capacitor .
- b) If P3.2 is still low (after discharging) - You have no capacitor connected
-B) receive Ready0 (measurement made) flag in 1..2 seconds after charging is started - this is good result to be displayed.
-C) receive Ready0 (measurement made) flag in 0,1...0,2 seconds after charging is started - this is "too fast" result.
You can display , and re-measure with next source transistor.

So Your target can be - finding source transistor with wich result is ready in 1..2 seconds, starting from strongest source.
And note - this time variable , mentioned above , is incremented in Timer2 interrupt, checked in mainloop.

Precisious results are better to get trough precisious parts:
1% resistors or better , better comparator .
I'm not sure how stable will be Your current sources. Maybe MOSFETs are better for Q5..Q9.
regars