Thanks for your reply.
None of the issues listed at the link you provided (macOS Sierra: If your Mac runs slowly) appear to be relevant. My Mac Pro has over 200GB of free disk space and 64GB of RAM and the activity monitor was not showing any unusual activity when the slow-down / hang issues occurred. I am not running any apps that require specific processors or graphics cards.
I have started up my Mac Pro in safe mode and the problem disappeared. I then restarted in normal mode and the problem did not initially recur. After a day of problem-free use of my Mac, the problem recurred immediately upon launching the Messages app from the dock. When I attempted to launch the Messages app, my Mac hung for about 25 seconds, then the app launched, but the part of the window where the messages should appear was blacked out. I tried to open a file in Excel 2011 and the Mac 'beachballed' while showing a blank open file dialogue window (as had been occurring previously).
My trackpad was still responsive and I was able to force quit Excel (it was not showing as non-responsive in the Force Quit menu, but I was still seeing a blank open file window and beachball). I then restarted my Mac in safe mode again. Once booted up in safe mode, I opened the Messages app, which still showed a black area where messages should appear. I opened Excel and was able to launch a file via the open file menu as normal.
I restarted my Mac in normal mode and all problems had again disappeared - Messages and Excel both worked normally.
I'd be grateful for any further thoughts on what might be happening, or advice on possible fixes. (I haven't yet tried setting up a 'test' user account, but will do this when the problem recurs.)