Instead of higher APR from staking for longer period, what do you think about witness and SPS voting power multiplier?
For example we can stake for 1 week, 2 weeks, 3 weeks, and so on with upper limit.

STEEM staked for 1 week has x1 voting power multiplier for witnesses and SPS
STEEM staked for 2 weeks has x2 voting power multiplier for witnesses and SPS
STEEM staked for 3 weeks has x3 voting power multiplier for witnesses and SPS
up to the upper limit

This will be very simple to implement (at least compared to separate inflation pools or multitiered privileges you propose above and I proposed before on thecryptodrive's post, vastly simpler than Dan Larimer's proposal while solving the same problems) and comes with completely custom stake periods. Power down will need a rework like example below:

• An account has 100 STEEM staked for 2 weeks and 20 STEEM staked for 3 weeks, they start a power down.
• After 1 week passes since power down is initiated the account will have 100 STEEM staked for 1 week and 20 STEEM staked for 2 weeks.
• After 2 weeks passes since power down is initiated the account will have 100 liquid STEEM and 20 STEEM staked for 1 week.
• After 3 weeks passes since power down is initiated the account will have 120 liquid STEEM