My battery just died yesterday (actually left the lights on). Took it out for charging today but my new automatic charger for detect such low voltage to begin the charging process. So, I had to hook it up to my great old Lucas charger (attached pic below) but only to notice there was no defection in the ammeter. I checked with my multi-meter and found the output was like just 0.24V, opened the case and checked the transformer an it was fine. Looks like a blown rectifier-selenium rectifier I guess (pic below). After a futile search found these rectifiers are no longer available, so finally got a KBPC2510 metal bridge rectifier. I've installed it on the battery charger and measured the out put at 6V and 12V setting gave me 6.9V/11.9V open circuited and when connected to the battery the outputs rose from 6.8- 8V for 6V battery and 14-15.8V for the car battery as it got charged .
Selenium rectifiers have a much softer I/U characteristic than silicium ones.
You can simulate the soft slope behaviour on the right by putting a few ohms resistor in series with each silicium diode. For your application a single resistor at the rectifier output may suffice. Mind the correct power rating and cooling for that resistor!