I ran into the same problem. To overcome the issue, I monitored the devices for about a week by logging in and checking the logs manually. Once I was sure they were reporting correctly, just very rarely, I created a false positive drop rule and added all the other devices that applied.
1) I haven't heard of anything like that. But you could have a script or monitoring software log into a device every 45 minutes, enough to cause the device to create a log entry. You could use something like Rancid to login and go to configuration mode, back out, then save the current running config. That should produce a log and keep tabs on your running configs, compare to previous configs if needed.
2) I have looked several times to see if I can change when that rule fires without any success. There may be a way to modify the system scheduler through the command line. I would think that same service runs the scheduled reports. But I'm just speculating and don't recommend messing with system parameters.