Hi,
Pardon my saying, better you than me: 1.5V and ~22mW...
Probably not a great circuit and certainly a relatively different idea to what you're doing, but for the sake of a picture speaks more than I can explain... Anyway, if you focus on the right-hand side (D2, R1, C3 and Rload), you can ignore T2 as far as I recollect - there's a diode to stop the capacitor leaking "backwards"...
Frankly, I have no idea but think it may well likely leak without a blocking device. You really need to use a Schottky do you? They leak loads compared to a bog-standard silicon diode.
What I was simulating last night looked like it would take several minutes to charge the 4.7mF capacitor, and that circuit had far more power at its disposal.
Charge pump or discrete voltage tripler sounds good. Home-brew/discrete voltage doublers are usually unwelcome for me as they have low output current capability (and rather inefficient) but it appears that maybe isn't an issue for you if it can charge the capacitor slowly.
This capacitor is for an MCU to finalise any tasks it was doing and shut down properly when the power goes or something like that? Just asking out of curiosity.
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Looking at your latest schematic again, wouldn't the battery be better off on ground and swapping the NMOS low-side switch for a PMOS high-side switch? What am I misreading about the schematic/functionality, please?