From my understanding, op’s problem is if he change system’s proxy setting he will lose connect to private network. This can be fixed by setting up detailed routing rules, which windows don’t allow. So you need a openwrt, or other router system. Furthermore, you can hack your router with openwrt or something like ASUS Merlin, which can solve almost everyhing related with proxy, regardless wether you have control on your PC.
Or you can try something like SSTap or netch, the are more lightweighted, but lack maintenance right now.