Hi Si,
I'm currently trialing both Squid & Tinyproxy in OVPS - as oddly enough, I'm hit with the same issue as you
Currently have Squid running ok, just https requests are proving problematic.
Working on getting squid up & running as a priority (along with the caching) on both windows & linux platforms.
Tinyproxy however, requires as postix platform, so not putting as much effort into that due to most sites not having the capability to run it.
As soon as I have a soloution, I'll let you know. Conversely, if you come up with anything....