Cheapest way to switch from Exodus wallet to something else
Exodus eventually answered this questions themselves, with a similar answer to that given by @McLeodX but specifically discussing import of BTC private keys rather than sweep or transfer.

In short, export BTC private keys from Exodus, import them into Bitcoin.info wallet, then use bitcoin.info to do future transactions with fees that can be adjusted.

I am sure there are other wallets for which this method will also work.