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I don't get it, honestly.
Just do split tunneling, and exclude a secondary browser or something. Way better setup, IMO.
Plus, you don't need to search for tons for extensions, which might not be official/trusted; and it's better to have a backup browser anyway.
I mean, split tunneling is a feature most VPNs supports, so why work harder for worse setup.
I just use FoxyProxy, which lets you use wildcard/regex rules to send different sites to different proxies (or none at all).
On firefox at least, you can also manually set a specific tab to use a different proxy.
"VPN blocked? Just turn it off"
Also report the issue to your provider so they can circumnavigate the bs.