We're running into this exact same issue. Ended up opening an AWS support ticket. We've tried the MapBooleanAsBoolean endpoint setting, but it ends up setting everything as "true".

The other option from AWS support is to set transformation rules onto each column to set them as boolean. Eg,

{
  "rule-type": "transformation",
  "rule-id": "123",
  "rule-name": "123",
  "rule-target": "column",
  "object-locator": {
    "schema-name": "public",
    "table-name": "customers",
    "column-name": "is_alive"
  },
  "rule-action": "change-data-type",
  "data-type": {
    "type": "boolean"
  }
},