There are a few ways.
All are (as others mentioned), resource wise, wasteful.
We do not profit from the Purge, some of those rescues from cages are good, some time uniques, especially named bearers and dancers.
But the boxes rarely pay for the repairs.

This one suggests, for higher tier purges, something of a maze with an open top. Use your own archers, well Armoured, to distract their archers. The Purge likes to go after doors, so put several along the path. As already mentioned, keep melee combatants on a very short leash.
If you are going to get in the mix, use a good AoE weapon.
Greatsword, Mace or Axe and Shield.
Something with wide arches and knockdown.
You will get mobbed.
Spear+Hammer+Sword is what this one frequently gets swamped with. Spears stutter, hammers sunder, swords knock down. Such an annoyance.

If you have ever played a tower defense game, it’s not dissimilar.

Weapons that poison my help you.

The Headhunters throw explosives, so perhaps you can use poison or tar shenanigans. This one hasn’t tried yet.