Couple of ideas:
Instead of having monsters divided by type (minion/brute etc.) divide them by squad. Put a marker on them (say a strip of blue post-it on a mini) and have balanced squads (2 minions, 1 brute, whatever) - roll initiative per squad, not creature type.
Other idea, as others have already mentioned, just pre-roll (ok - just pick a number) initiative for all baddies pre-adventure. I don't know why they just don't replace initiative mods in monster stat blocks with a straight "acts on intiative 14", especially for non-elites/solos.