Faster settling time for near DC pole low pass filter
Speeding up the 'start up' of a long time constant filter, by switching a lower R, or putting a schottky diode across the R, is a well known tried and tested thing to do. 

Your voltage reference only has to avoid damage if it's too heavily loaded during start up, the output voltage is going to be wrong during start up anyway, so check its safety into a sort circuit, not the maximum current for regulation. As the charge current drops, it will come into regulation. 

OTOH, buffering the reference during start up will allow a higher charge current for your filter FBC (very large capacitor), and the buffer does not need to be a precision type, as the output voltage will be wrong during startup.

If you consider a buffer connected by two back to back diodes to your filter, then it automatically disconnects when the voltage is close enough.







simulate this circuit &ndash; Schematic created using CircuitLab

Analysing the operation. The filter is R1, C1. 

Let's assume C1 is the same voltage as the reference V1, that is, the filter has settled. The amp -ve input will be at the reference voltage, so no current flows through R3. Its output will be at the reference voltage, so no current flows through the diodes. With normal minimal amplifier voltage offsets, little current flows through R3.

Now during startup, there will be a large error voltage on C1. The opamp amplifies this by the ratio of R2/R3. If the output voltage >0.7v, so if the error voltage is >70mV, one diode will conduct to charge the capacitor quickly. Once within 70mV, the diode stops conducting, and the final filter settling occurs in the normal way through R1.

The size of window outside which fast charging occurs can be controlled by the gain of the opamp. With 100x gain, the fast charge window would be 7mV. The limit to how small this window can be is given by the input offset error of the opamp, you do not want it turning on once the filter has settled.