May be you can try to add cat's paw or vampiric nature to your build, that way you would survive the first wave, and being in full BB the dps should be enough to finish Drostan before a second wave.
Also, if avatar + liberation doesn't bring enough dps/drain to survive first wave, try to stack Kidney shot or Grey lotus pet (or both) on top.
Besides DW, essence detonation will be very effective on the rats because of it's aoe. Save it for the spawn and place it on Drostan.