"Error while trying to synchronize audio and MIDI" is a familiar Logic error message—unfortunately, though it seems to suggest a specific issue, most of the time it doesn't really point to anything in particular. I also have Logic 10.4.5 & Mojave 10.14.5, and a similarly spec'd 2015 iMac, so I guess the basic rig should be fine, in theory..
It certainly wouldn't hurt to reinstall Logic; before doing that you might want to try blowing out Logic's Preferences (save the old files in case there's no difference) and test for a while—corrupted Preferences can cause all sorts of issues..
Reinstalling the OS could be a bigger deal—if you did decide to go that way (Apple would probably suggest that), make sure you have a current bootable clone backup first.
But before you pull the trigger on any major reinstalls (or in case that didn't solve the problem), here are a few other things to consider, as far as troubleshooting..
- In case it really is related to the audio engine, try running Logic with the built-in audio driver instead of your interface's third-party driver
- If the problem occurs only when plug-in windows are open, it could be a graphics issue.. Does it happen in sessions that use only the built-in Logic plug-ins, or only when third-party plug-ins are involved? You might want to try removing all third-party plug-ins temporarily and test for a while; if the problem goes away, then it's most likely a third-party plug-in compatibility issue—add them back in one/a few at a time to see if a particular plugin/brand is responsible. If the issue persists with just the Logic plug-ins, then there might be an issue with the graphics engine, depending on the graphics card in that machine; there have been Logic issues with plug-in graphics over the years, but I can't recall the specifics..
- In 10.4.5 Logic changed the graphics handling in the mixer displays, citing performance issues with the mixer open; maybe try shutting the mixer panel/displays to see if that affects things in any way..?
- A number of people have reported issues with 10.4.5 and 10.4.6—just as a test, you could try rolling back to 10.4.4 (you do save previous versions when updating, at least for a while?) ;-)
- A standard troubleshooting test is to create a new (temporary) User, and try running Logic in that User space; if the problem goes away, then something in your User space is incompatible or corrupted
Unfortunately, escalating performance problems and crashing that are not tied to any new software or upgrades could indicate general Logic/OS corruption. You might want to try resetting the PRAM (I know, everybody always suggests that and it rarely has any effect, but it couldn't hurt). Running analyze/repair on the drive(s) also probably wouldn't hurt, I guess (though in my experience disc repair rarely solved any problems detected—wiping the drive and restoring files was always a better solution to drive corruption issues).
Good luck with your troubleshooting—I've had to go through that at times, and I feel your pain; hopefully you'll find a solution sooner rather than later..