At 135mA the voltage drop over the BAT30 is between 500 and 580 mV. That's very large for your circuit.
You could use mosfet switches to simulate diodes.
There are also ic's for switching voltages without voltage drop. Search for "ideal diode".
For example the LTC4411 is made for a situation as you have !
As a bonus you get a status line telling which power source is used at the moment.