I will not recommend anyone to migrate the wallet or import the private key, it will be better to transfer the monero instead to the new wallet. Also because Exodus is a close source wallet.
In fact, this only applies for users who won't manage to send the coins on time. If a user wakes up one day after exodus has stopped their monero support, the only way they will (hopefully) have to save their coins should be to migrate their wallet. This is because the seed phrase that Exodus provides can't be used in other Monero software wallets.
I think what Charles-Tim means is that you shouldn't use the same wallet on other wallet software; instead, once you import it to other wallet software, transfer it immediately to a newly created wallet.
Feather is a good option as you suggested above for the desktop lite version of the Monero wallet, but the problem it doesn't have a mobile version yet, so a much better alternative for mobile users is the Cake Wallet.
The good feature that I want in Cake Wallet is the advanced privacy option, where you can enable TOR.