If you overcharge, you will cause the batteries to vent. NiMH are the most difficult of all the common rechargables to charge correctly. Read what battery university has to say.
A trickle charger is the only safe option for a simple charging circuit.
The only other option is to use a timer, but that is fraught with danger. If the batteries are not fully discharged when you start they will overcharge and vent.
The capacitor across the battery is doing nothing. It is just going to track the battery voltage, not providing any additional charge current. If you put the diode to the capcitor then to the resistor to the battery, the capacitor will charge during the time that the input waveform is less greater and discharge into the battery when it is lower. This will give you about 16V for charging from a 12V supply.
Now, to calculate the resisstor. The charger voltage is 16V. The battery voltage is 4.8V, so the difference, which must show up across the resistor, is 11.2V. The current desired is 800ma / 20 = 40ma. So
V = I R
11.2 = 0.04 R
280 = R
Bob