To increase the current you would need to increase the capacitor. With 120 V, 60 Hz power there will be about 30 mA with that capacitor.
You need to limit the current with all LEDs. They don't "draw" current like bulbs do. If you change the LEDs and make no other changes, the circuit will still limit the current to 30 mA
However, LEDs vary a lot in how efficient they are. If you are changing the LEDs, you could try them with the existing capacitor, and they may be much brighter at about 30 mA than the existing ones.
The current rating of the LEDs is their maximum, and they will generate a lot more heat at 100 mA than they will at 30 mA, so you might get a problem if you do increase the current a lot. I suggest that you get another couple of 0.68 uH capacitors (rated to at least 1.5 times the mains voltage) and put them one at a time in parallel with the existing one.
The 1 M ohm is there to discharge the capacitor when you unplug. You don't need to change that. The rectifier does not need changing as just about all rectifiers are rated at 1 A or more.