Mac – Cant delete Time Machine .inProgress file

What's in the trash? Are you sure it's all stuff that can/should be deleted? If so...

Try right-clicking the trash icon, hold the option key, and then click Empty Trash. This should attempt to force-empty the trash.

If that doesn't work, open the Terminal and enter sudo rm -rf ~/.Trash/*. The command rm -rf is a dangerous one since it will immediately delete anything without worrying about what it is. In the case of emptying the trash, that's what you want. I suggest you use copy-and-paste to enter the command if you're not used to using it, just to make sure you don't instantly delete anything other than what's in the trash.

I believe this is a staleness prevention. That whenever there is too long between backups Time Machine uses a more thorough way to ensure that the backup is complete.

It is my understanding that the 40 GB is a "this is how much we consider for backing up" and that the actual data transferred may prove to be a lot less if the files turned out to still be identical.

Based on your description I believe that you have reached a point where you need to let your Time Machine backup catch up - work on its own until it is done, if at all possible. If you cannot wait for that, perhaps now is a good time to buy a new drive and use that instead and have the old drive as a backup backup.