In my application I would like to use it to drive a high impedance input, and the pull up current for the open drain is significant compared to the rest of my circuit.
There is no push-pull version of the ADCMP380 and no exact replacement option as well. But you may want to check these push-pull comparators also by Analog Devices: ADCMP356, ADCMP371, ADCMP380.
ADCMP356 has 0.6V on-chip reference and has non-inverting input. But if you require a specific reference voltage, then the general purpose ADCMP371 and ADCMP380 may do, in which you have to use external reference. ADCMP380 has shutdown pin if you also require such.