I tried the first but it did not work. The second seems a bit drastic. It seems to me there should be a less invasive solution.
Assuming it is an IMAP account solution 2 is a piece of cake and you will not lose a thing in the process. I have had to do that on more than one occasion when I was having problems with an account. Just be sure to get a screenshot of the account settings before you delete the account. The password will be preserved in Keychain if you have forgotten it.
If it is a POP account, then all bets are off as you will lose all the data in the account mailboxes. You can however create mail folders "
On My Mac" and move the downloaded POP messages there —
BEFORE you delete the account.