This was the error that I was seeing (in Safari)...

I figured since using a different browser helped the situation that it might be something to do within the browser itself. So back in Safari I went over to the Web Inspector and had a look in the Storage tab. I noticed that there were many (many!) cookies stored for the domain that was showing me this error...
I thought that I'll try and delete all of these cookies and see what happens. Lo and behold, I was able to log in again! Logging out and logging back in worked too. However when I logged in, closed the window (without quitting Safari) and went back into the web application after some time - the same error sprung up.
It looked like there was something in these cookies that was becoming stale and causing OAM to error out. That's as far as I went with my debugging since logging out instead of just closing the widnow/tab was a good enough workaround.
I'm not sure if the issue lies inside OAM or with Safari but given this was an an application upgrade on the web application side and Safari remained the same as before, I'd bet the issue is with OAM.
-i