I am looking for a freeware local proxy to perform proxy-chaining with HTTPAUTH.

To explain my situation:

In my workplace I am forced to keep switching between several internet-connected apps, and thus everytime I have to type in the credentials (or, at least, click on 'OK' to send my previously-saved credential). To make matters more annoying, the proxy login times out every 30 minutes, requiring me to lather-rinse-repeat the whole annoyance.

I'd like to just point them all to a locally installed proxy which will on its own perform the required HTTPAUTH against the corporate proxy.

I've tried Cntlm, but it always fail to authenticate (and according to this thread, that is due to the proxy using HTTPAUTH which is not supported by Cntlm)

Any suggestions?

ETA: I found Polipo, but it's kinda wonky on Windows. Especially if I visit a new URL, and the DNS server is a bit slow, then Polipo will simply drop/refuse the connection. And I have to put my password in plaintext. If there's a better suggestion, I'm all ears.