HI there @barrycox 
I’m sorry to hear you are having some trouble set this up correctly, but it does seem like we’re almost there from where I stand 
Since you are able to get the try-it-yourself result to work, I would say your JSON formatting is on point in this query:
mutation { change_multiple_column_values ( board_id: 655318672, item_id: 662694544, column_values: “{\“date4\”: {\“date\”: \“2020-08-04\”},\“next_arr__days_7\”: \“9\”,\“property_id\”: \“1289\”,\“person\”: {\“id\”: null},\“numbers2\”: \“1.50\”,\“departing_rez\”: \“5146\”,\“status\”: {\“index\”: 1}}”) { id } }
One thing that I’ve noticed in the very first query that you are trying to send is that the whole query is formatted as JSON, whereas I believe only the column values you are trying to send should be formatted as such. Does that make sense?
EDIT: Turns out I was not entirely correct about this, since the whole request body is JSON.
@dipro has helped me out here and his insight is that the quotes inside quotes should be double-escaped:
{“query”:"mutation { change_multiple_column_values ( board_id: 655318672, item_id: 662694544, column_values: "{\"date4\": {\"date\": …
To save some hassle, we recommend using GraphQL variables to handle this. That way, you’ll be able to send the column values as JSON and the app will do the escaping for you. There is more information on this topic in our tutorials as well:
Also, here is a helpful post that might help:
cURL examples for API v2
-Alex