LDO regulator stability with bypass capacitor
MIC5205 using 1nF bypass cap can be modelled by a 0.01R resistor in series with an inductor of value 0.6 ... 1.5 µH (it depends on DC current).

Using these parameters, you can simulate its stability with the ESR of your tantalum caps. Set the transition from regulator to cap below 40 kHz to avoid the regulators' second pole.