Incognito mode is nice, but your ISP sees the traffic. VPNs are pretty neat, but you'll solve CAPTCHAs all day. Why not pick the best of both, with an incognito-only VPN?
The requirements are a SOCKS5 proxy server and a secure tunnel, such as WireGuard with allowed-ips w.x.y.z/32 (IP address of the proxy) or ssh -D1080. There are commercial VPN providers with WireGuard and SOCKS5, or you could self-host. The Incognito Proxy extension solves the sub-problem of "How do I configure a SOCKS5 proxy specifically for Incognito tabs?"
More generally, this extension configures proxy settings. It has few features, but its namesake feature is the ability to configure different proxy/direct settings for regular windows and incognito windows.
I've tested the "Incognito to SOCKS5 over WireGuard" config on a Chromebook; it is unobtrusive, survives rebooting, and I can still LAN print. Annoyingly, Chrome's WireGuard config forced me to pick a static DNS server; 0.0.0.0 worked at first, but not reliably.
The disable_non_proxied_udp option can prevent WebRTC from leaking your non-proxied IP address.
Please steal my code, because 'incognito proxy' is a good feature. I copied it from chrome-extensions-samples and made minor improvements.
The relevant API call is chrome.proxy.settings.set({scope: 'incognito_persistent', value: ...})
https://chrome.google.com/webstore/detail/incognito-proxy/odkbcffeaickjalieahlneeehkgjpade
Link to bug: https://bugzilla.mozilla.org/show_bug.cgi?id=1526299
FoxyProxy plans to implement this feature using a different API: foxyproxy/browser-extension#33
