Using REST POST to edit a Multiselect Additional Field

I have been working on a way to create new requests using the POST function of the REST API. So far I have had no issues setting info in the default fields (Subject, Description, etc), but I'm not able to get a custom Multiselect field to accept data. I continue to get this error:

"{"response_status":{"status_code":4000,"messages":[{"status_code":4001,"field":"udf_multiselect_309","type":"failed","message":"Unable to parse the JSON"}],"status":"failed"}}"

I found a document that has been very helpful for all the default fields which also contains some information for how to use custom UDF fields, but it doesn't appear to be helpful. Here is a small example they've given.

"udf_fields": {
"udf_ref1": {
"name": "test-name",
"id": "2470322684475602"
},
"udf_boolean1": false,
"udf_long1": "2136851967326526",
"udf_date1": {
"value": "1478758440000"
},
"udf_double1": "test-udf_double1",
"udf_char1": "test-udf_char1",
"deptheadid": {
"name": "test-name",
"id": "1975292840863883"
}
}

My Multiselect field has a Column Name of "UDF_CHAR1", so it seemed possible to use that portion of the snippet as it is, but when doing so, I get the error "Extra key found in JSON". So I tried to use the API Field Name listed in the Additional Field - Incident page, which is "udf_multiselect_309" and got the error at the top of this post.

My REST "input_data" line at fault is: