You need to specify header as 'HTTP_X_HTTP_METHOD_OVERRIDE' instead of 'X_HTTP_METHOD_OVERRIDE' i.e. add HTTP_ at the beginning of the header.
header = {'HTTP_X_HTTP_METHOD_OVERRIDE': 'PUT'}
response = client.post('/model/1/', content_type="application/json", data=post_data_clean, **header)
From the Django documentation:
HTTP headers in the request are converted to
METAkeys by converting
all characters to uppercase, replacing any hyphens with underscores
and adding anHTTP_prefix to the name. So, for example, a header
calledX-Benderwould be mapped to theMETAkeyHTTP_X_BENDER.