How to backup paper wallet digitally I'd like to move some bitcoin off an exchange and into a paper wallet for long term storage, but looking for ways to backup the keys in case of theft/fire/stupidity.

My thought was to (on a new offline machine) create the wallets and put the keys in a text file, as well as print. Encrypt the text file with GPG and record the passphrase in my password manager and on the paper wallets themselves.

Is it reasonably secure to then copy and store that encrypted file on USB, Dropbox, email etc?
I wouldn't use Dropbox. Use 2 encrypted USB drives or harddisks and store both on separated locations. Storing it on 2 locations prevents it to be damaged during a fire or any other event or robbery.

The precautions to take depends on the value of your wallet ofcourse. A high value means higher precautions.

For example, you'd store $30 cash in your wallet and $1.000.000 or gold bricks in a safe or trusted bank with goverment insurance. 

If you have a $xxx or $xxxx amount, store an usb at your home and another one at your work. If the amount is higher, i'd spend some money on a safe.