How do I get into a disabled iPhone using iCloud log in without losing data that's in the phone?

There is one, and only one way to reset a disabled device. You must erase it by restoring it in itunes. This is explicitly by design so that nobody, no one at all, can gain access to a disabled device with intact data.

You cannot backup a disabled device. You cannot do anything with a disable device until it is reset by erasing it.

If the device is disabled by entering too many passcodes or for any other reason, and there is not a backup already in place, data loss is inevitable. There is no way around that reality.

Too late for that now. Backups are needed before a catastrophe.

In order to back it up you must be able to turn it on.