Low Current and Voltage Power Supply ORing
There might be some possible clever scheme using MOSFETs, but most likely the additional control circuitry will also have some leakage that will make it as inefficient as the simple scheme you planned.

I am sure the solution here is simply to find the appropriate components that, in the end, will lead to an acceptable compromise. For example:

Regarding the diode:

BAT54 has 0.5µA typ leakage at 25°C and 5V reverse voltage. The drop is higher than with more beefy schottkies though. About 0.2V at a 0.1mA. So if you keep using a 2.5V regulator, you may end up below the 2.4V min voltage required, so:

Regarding the voltage regulator:

You could use a 3.0V LDO with ultra low quiescent current to compensate for this higher diode drop. You can actually find some rather easily: TPS78330, for example, has 0.5µA Iq. NCP4681/NCP4684 claims 1µA typ. MCP1710 claims 20nA (!).

Just spend some more time on google/mouser/digikey and reading datasheets. What you want is achievable the way you planned it, with the right components.