Simpler method:
Paper wallet.
Until you want to spend some of it.
Trezor is as secure and also functions as an offline computer to sign transaction so you can spend your coins.
You never have to back it up and it discourages address reuse.
Best wallet at this time.
Spending from a paper wallet is not hard at all.
Trezors are expensive... for normal expenditures it's not worth the money and effort. For long-term storage of large amounts, paper wallets are virtually free and safe as can be.
How do you
easily spend/move/sweep your BTC from a paper wallet
without ever exposing the private key?
The private keys never leave the Trezor and are never exposed - that is the purpose of the Trezor. Trezor may be too expensive for storage and use of small amounts of BTC but for large amounts (10(?), 50, 100, 500, etc. BTC) it is perfect. For small amounts the paper wallets are fine and as you said, free.