Can't get "Update Flow Element" to work

Has anyone been able to successfully use the Update Flow Element request? I can't see what I'm doing wrong....

URL

One thing not mentioned in the API documentation is that I'm pretty sure the path param for

flow

must be

FL_1

(since this is the root).
https://{datacenter}.qualtrics.com/API/v3/survey-definitions/{survey_id}/flow/FL_1

Body

The body also seems straightforward, using an array containing objects representing each flow element you want to update.
[
{
"Type": "EmbeddedData",
"FlowID": "FL_3",
"EmbeddedData": [
{
"Description": "Existing",
"Type": "Recipient",
"Field": "Existing",
"VariableType": "String",
"DataVisibility": [],
"AnalyzeText": false
},
{
"Description": "New",
"Type": "Recipient",
"Field": "New",
"VariableType": "String",
"DataVisibility": [],
"AnalyzeText": false
}
]
}
]
The element I want to update (FL_3) is identical to how it looks in a getFlow response, except I've added an embedded data field.
Get Flow response:
{
"meta": {
"httpStatus": "200 - OK",
"requestId": "3cb02149-d390-4017-9167-736762b21f57"
},
"result": {
"Type": "Root",
"FlowID": "FL_1",
"Flow": [
{
"Type": "EmbeddedData",
"FlowID": "FL_3",
"EmbeddedData": [
{
"Description": "Existing",
"Type": "Recipient",
"Field": "Existing",
"VariableType": "String",
"DataVisibility": [],
"AnalyzeText": false
}
]
},
{
"Type": "Block",
"ID": "BL_bpUwj7v7fYQdfKe",
"FlowID": "FL_2",
"Autofill": []
}
],
"Properties": {
"Count": 3,
"RemovedFieldsets": []
}
}
}