You don't say what version of Finale you're using, but if you're on Catalina, then Finale 26.3 and higher are supported and should work well. There's nothing particular about Catalina that should cause it to make 'delays', so this problem could be solved some other way.

2015 Macs can be upgraded to macOS 12 Monterey. I'd recommend upgrading to that, and then keeping all your software as new as possible. 

Problems tend to arise when you have a large 'age gap' between your OS and your apps. 

So  now the new catalina is causing a dangerous delay in moving notes and scanning the score.

Nope. Not saying you don't have a problem but it's not what you think. If you have any 32 bit plug-ins or apps trying to load, this is the most likely cause. Catalina is 64 bit only and all apps and plug-ins must be 64 bit to run—no exceptions or workarounds. For that reason, Finale 2014 and earlier cannot run over Catalina or higher. 

Finale 26 and 27 were extensively tested over MacOS 10.15 Catalina (which will be will be 5 years old next month). I had no problem running 25 either. 27 runs just fine on my 2012 MacBook Pro—looking at it right now. Catalina is the last MacOS that MBP supports without a hack.

Catalina is the minimum MacOS that supports 27. Depending on the build and model, a 2015 iMac can run either MacOS 11 Big Sur or OS 12 Monterey.

There's always the possibility that an 8 year old iMac has developed a drive problem that will need to be diagnosed and repaired. Without having it on my bench, I don't wish to speculate further. The right replacement drive can have a 2015 iMac running 3x–10x faster than was possible when it left Apple depending on what they installed in yours.