If you set the default device down alert rule delay to 600s, or perhaps 605s, it should do what you want. This will span 3 polling attempts (default interval between is 5 minutes). If the device comes back up in 8 minutes, the third poll should get a reply. Adding a few extra seconds will help prevent one slow ping response from firing a false positive alert.
Filter the devices in that alert rule. Then add a new version of the same rule with a longer delay for the other devices.
The device down rule was one of the defaults when I installed, but it has been many versions ago. If you don’t see it in there you can create a new rule from the collection and it should be near the top of the list. Just try using the rule as it’s configured by default but change the Delay to 605 and test and see if it does what you want. The main thing to remember is that your polling interval determines how finely you can tune it.