Did that and AppleCare has not offered any help other than asking me to temporarily downgrade to 7.1.2 (They are aware of the reboot issue)
That would not happen. Apple does not support downgrading software on iOS to previous versions.
What they would ask you to do is restore your iPad to the factory settings using iTunes, and then set it up as a new iPad without restoring from any kind of backup. There is some sort of software issue/conflict/corruption on your iPad, the only way to fix it will be to restore to factory settings. Downgrading back to iOS 7 would also possibly fix it, but this is a problem that just isn't happening with most iOS 8 users.
We don't have Apple Stores in my country, yet. So we do not get world class service Apple is known for. Even if they take my iPad in, I will get replacement only after 10 days.
There's no need to replace a device for software issues. You'd restore the new device from your backup and the same exact issue would come back.
By the way, even one of my friend's iPad Air had a kernel panic and rebooted itself. He said it happened after 2 days of heavy Safari use. I am pretty sure that sooner, many people will find out that this is a real problem.
There are few isolated posts about spontaneous reboot on this forum as well. Just that they have not received enough attention.
There are many millions of iOS 8 users. There will be posts about kernel panics no matter what. But because the posts are so few, and so scattered and rare, it shows that it's not a problem with the iOS 8 software, it's some app, some website, or some other sort of issue unique to your device.