I don't see why immigrants couldn't turn up on our doorstep from other races, looking for work, rather than having to buy them via the broker all the time. You could have both. Other fantasy games frequently have multiracial settlements with one particular culture. I would suggest as well that one option for dealing with newly-discovered animal men tribes could be to make an agreement with them that you will feed them and provide protection for them if they agree to fight for you or do physical work. They will then operate autonomously and keep to their own stuff, but they'll do the jobs you've asked them to do. A noble or similar could be appointed to deal with them, a diplomat for instance. Learning their language would be an essential skill for him.
I also remember having a large discussion about this kind of thing in a thread a long time ago. I ended up getting into an argument with someone over how I thought different races could be better at doing different jobs, so tigermen workers may be excellent trackers from their hunting and also excellent warriors for their agility and skills in wrestling/restraining their prey, but something strong like a troll would be superior for hauling. Elves could be very useful animal trainers and rangers, due to their knowledge of animal men languages and such. It would mean that different types of animal men actually differ on a kind of social/cultural level rather than a physical level too.
Here's a story for how this could go. A goblin army has met the Dwarves on the battlefield and are making ready for the great clash of shields and swords. The Dwarves are outnumbered but foolhardy; they do not seem discouraged by the hide and leather clad baying masses before them. The Dwarven general stands atop a small hill, brandishing his blood-spattered battle axe at the Goblin leader. The Goblin leader deems this to be a show of bravado, and believes the Dwarves to be making a last stand, hoping that their superior troops will hold against the overwhelming numbers of goblins. The goblin general even chuckles to himself, a sound like gas escaping from the mouth of a corpse. He knows he will be victorious.
However, much to his amazement, the Dwarven force begins to slowly advance. They begin to sing monotonously, almost like an incantation or chant. The Dwarven general raises his battle axe into the air, throws up his head to the sky and bellows a command through his flowing beard. The Dwarves break into a charge, battle axes raised, the song becoming a deafening roar. The Goblin general is utterly shocked by this suicidal charge, and bellows his own command to his men. The two forces clash together and the battle is bloody. Severed heads and limbs sail through the air in arcs of gore, goblin and dwarf alike. It remains far closer than the Goblin general realised, with the chances of victory lying in any side's hands. Suddenly, a goblin scout shouts to the general. The general looks. Ten figures on the tree line to his left, dressed in the light armour of the Dwarven culture, but with helmets that seemed to have removeable grates at the mouth area. The figures are several feet taller than any dwarf on the battlefield, and move almost silently. The Dwarven general suddenly gives a high-pitched shriek, rather like a cat. The figures suddenly fall onto all fours. They tear open their mouth grates revealing chops and fangs. They charge at the goblin general and his entourage at a speed he never deemed possible. The goblin general screamed and fell from his beak dog mount as the cheetahmen bore down upon him, tearing at his throat and eyes. As his life blood poured into the soil and he was torn to shreds, he saw his men break rank and retreat. The cheetahman on top of him hissed something to him. A paw with claws extended suddenly slashed across his face, tearing his brains and ending his wretched life.