After emailing the Solr user mailing list, there are TWO things you need to do:

1. You need to have uninvertible=true, AND

2. You need to explicitly specify an analyzer for fields, even though they're based on TextField.

Here's what wound up working:

curl -X POST -H 'Content-type:application/json' \
  "http://localhost:8983/solr/$COLLECTION/schema" \
  -d '{
    "add-field-type": {
      "name": "multivalued_texts",
      "class": "solr.TextField",
      "stored": true,
      "multiValued": true,
      "indexed": true,
      "docValues": false,
      "uninvertible": true,
      "analyzer": {
        "type": "index",
        "tokenizer": {
          "class": "solr.StandardTokenizerFactory"
        },
        "filters": [
          {
            "class": "solr.LowerCaseFilterFactory"
          }
        ]
      }
    }
  }'