This isn't exactly an answer, more of a workaround that I came up with, that I've decided to post since this question hasn't yet received any responses, and it may help anyone else trying to achieve the same thing.
The workaround is basically to use the httplib and urllib modules to build and make the PUT request instead of the HTTPClient module.
import hashlib
import httplib, urllib
....
params = [("title", "Here's the title"),("content", "Here's the content")]
params.sort(key=lambda param: param[0])
ps = ""
for param in params:
ps = ps + param[1] + ":"
ps = ps + "myapikey"
m = hashlib.md5()
m.update(ps)
params.append(("signature", "myusername:" + m.hexdigest()))
params = urllib.urlencode(params)
print params
headers = {"Content-type": "application/x-www-form-urlencoded"}
conn = httplib.HTTPConnection("www.mysite.com:80")
conn.request("PUT", "/api", params, headers)
response = conn.getresponse()
print response.status, response.reason
print response.read()
conn.close()
(Based on the example at the bottom of this documentation page.)