You can probably set your pi up as a gateway itself, and proxy everything though it. I've never seen any device that doesn't trust the default gateway given by

You can probably set your pi up as a gateway itself, and proxy everything though it. I've never seen any device that doesn't trust the default gateway given by the router, nor have I seen any that try other addresses if the default gateway doesn't exist. I don't have any more information on that, though. I would like to set up a caching proxy as a gateway, but iirc squid doesn't like https in any form. I've had too many times where some app needs to download the same large file on every run, or I want to use some massive webapp in private browsing mode.