You are connecting one VPN via Tunnelblick inside of another VPN (via AnyConnect). That is very tricky to set up, but it must have been set up correctly at one time since it worked for you for many years. Since it was working, any or all of several things have probably changed: your version of OS X, your version of AnyConnect, and your version of Tunnelblick, and the router that you connect to the Internet with.
This isn't the sort of thing that I can debug, since I don't have AnyConnect. And it seems that AnyConnect is the problem, since it is AnyConnect that hangs.
When I wrote suggesting that you could "simulate a Wi-Fi problem using Ethernet by simply disconnecting the Ethernet cable", I meant (and should have said directly) that you could disconnect the cable, and then reconnect it, to simulate a temporary Wi-Fi problem. If you disconnect from the Internet, OpenVPN may (depending on the configuration) just keep trying to reconnect. So when you say it "hangs for a very long time", and if by "it" you mean the connection, that is to be expected. But Tunnelblick shouldn't hang in the sense of not responding to clicks.