Can I offer free shipping above a set amount in one region only?

Yes. Each method in a shipping zone has its own threshold:

1. Go to Plugins → Shipping Zone and click Edit on the zone for that region.
2. On the method, fill in Free above cart total, for example 500.
3. Click Save zone.

Customers in that zone pay the method's normal cost below 500 and nothing at or above it. Leave the field empty on your other zones' methods so they always charge.

Keep the free-shipping option on Settings → Store Settings → Shipping Setup switched off if you don't want it to apply to addresses outside your zones.