I suspect this is what is happening:
On the A range, the shunt has a low impedance and with AC currents in the mA range, measured voltages are very low too. The true RMS to DC converter has a longer settling time with low voltages, hence the behavior you have observed.
On the mA/uA ranges, the shunt impedance is higher and thus measured voltages higher too, shortening settling time.
I'm not sure what converter the 87 V is equipped with, but it probably behaves in a similar manner.
Here is the graph for typical settling time versus voltage: