UPDATE: This is FAR easier to do in a strongholds match--assuming you survive long enough to get T3 units, but that doesn't take long and as long as you're trying to capture stuff actively, you won't get wiped out! It's somewhere around 5 minutes until T3 units are unlocked in Strongholds, and then you could build every type of unit.
If you prefer a far less stressful way of doing it though, just follow the original idea:
You can easily do this in a Skirmish against an Easy AI; pick any map, Deathmatch, turn Fog of War off, resources to max, and just build on all the bases then put a few turrets and shields on each base, build up your extractors and harvesters, then focus on building every unit.
I generally just built all units from the base closest to the enemy AI in case I wanted to wipe them out afterwards.
You will need to reach level 3 with your unit building base in order to bring in the Scarab. You don't have to reach level 3 for the other special units though.
Special units are trained from the War Council, and each leader has a different special unit.
The Fortress also has a slight variation between leaders
Unless otherwise noted, all leaders have these units:
War Council:
*Honor Guard -- Shipmaster exclusive
*Warlord -- Decimus exclusive
*Atriox's Chosen -- Atriox exclusive
Scarab
Fortress(Main Base building):
*Chopper -- Decimus and Atriox exclusive
*Ghost -- Shipmaster exclusive
Grunt Squad
Raid Camp(infantry):
Jump Pack Brutes
Suicide Grunts
Elite Rangers
Hunters
Apex(aircraft):
Engineer
Banshee
Shroud
Blisterback
Foundry(vehicles):
Marauder
Reaver
Locust
Wraith
A total of 19 units to build, and you will have to play each Banished leader in order to get the unique units.