Eliminating negative output voltage in a LM317-based power supply adjustable down to 0V
You changed the rules of the game, so no wonder it does not behave the same. You changed JFETs so the idle current is increased, and what was once a -10 volts is now -13 volts, just about matching the error you are getting.

Simple fix is to put a resistor of 50 to 100 ohms in series with your negative supply output, then add a 10 volt 1 watt zener diode to ground to get things back in the ballpark. Remember to get the zener black band pointed to ground.

Add a 1K trim pot below the voltage adjust pot and trim it so the most negative voltage you can output is maybe -.01, just to verify you can get down to 0.000 if you have to.  If you want more stability replace the 10 volt zener with a LM431 or a TL431 with gain set to 4 - 1 (the ref voltage is 2.50 volts), to get a stable 10 volt clamp for both current and voltage regulation.

You should not have to tinker with anything else, though having the original JFETs in the schematic would have saved you some minor trouble. Remember that even though you can force the -10 volts to be just that, the change in FETs affects voltage at certain points because of a change in bias current. You may need a 1K trim pot on the current adjust as well.