Check 1TB folder and only copy modified files

I would like to know if this is possible?

My Home folder is currently at around 1TB and what I would like to do once a day is to run a rule that checks that folder and all modified/new files will be copied to a specific location and new folder while maintaining the folder structure and giving that new folder the current date.

I would like to use a service such as Dropbox/Google Drive/iCloud to store only modified files, not the whole Home folder, similar to how CarbonCopyCloner creates the SafetyNet folder inside the backup disk (for those familiar with that app).

So for example if I have 10 files on my Home and I modified 2 of them, once I run the rule, it would create a new folder inside my DB/GD/iC folder with the current date and with only those 2 files. And it would keep doing this for every time I run that rule.

Is this possible? I don't have a way to have a remote backup at the moment and this is the only alternative I can think of, but I don't want to pay for space (DB/GD/iC) I don't really use and I also don't want to put all my files in the cloud if I don't have to.

You would need several things:
1 A rule to tell Hazel to go into subfolders.
2. A rule to copy the file.

Rule #2 would use the Copy action to copy to the main destination folder. It would then use Sort into subfolder to sort into a date folder.

What I'm unclear on is how you intend to maintain the folder structure when you have a dated folder. You would need to clarify this as how to handle this would vary greatly depending on the details.