I really like the idea of a quick power-down option at the cost of a fee that gets redistributed to holders or burned. Like most, I'm not a fan of a power-up & reward claim tax.

Just thinking about it briefly, I would model it with half being burned / half being redistributed to HP Holders

Instant Powerdown: 8% Tax (4% gets burned / 4% gets Distributed to HP Holders)
24 Hour Powerdown: 6% Tax (3% gets burned / 3% gets Distributed to HP Holders)
7-day Powerdown: 4% Tax (2% gets burned / 2% gets distributed to HP Holders)

Also, allow accounts to have the Quick-power-down disabled (or even have it disabled by default) with an option to turn it on for instant/24-hour/7-day which takes at least 7 days so it adds to the security in case accounts get hacked.

Maybe a bonus % on distribution for stakeholders can be put in place based on how long HP has been in place to extra rewards the long term hodlers giving everyone an incentive to those powering up to keep their stake in place even though that would make things more complicated.