It seems that my project files sizes are rather on the large size - between 35-80Mb
In my experience this is definitely your problem. I've written extensively on this topic in the past; it boils down to Apple's implementation of autosave, which updates the project file after every action (and blocks the application from doing anything until it is complete). This causes the spinning wheel to appear as well.
Your only option (at the moment) is to split your projects into smaller projects. That means to copy/paste sections of the original project into new projects. Your goal, until an update from Apple which hopefully will allow the large project file sizes, is to keep your project file sizes to no more that 30MB. When splitting them up, give yourself some headroom. So try getting each project file down to ~ 15MB, no more than 20MB. So split the 35MB projects into 2-3 new projects, and the 80MB projects into 4-5 new projects. If you select parts of a project and then use copy (command-c), you can then create a new project, and paste right into it (command-v). After you've done this successfully for the entire project, you can delete the original large project.