The instructions for 2020 Form 5329 say that you can report an Other reason exception on the amount of the coronavirus-related distribution.  However, the draft instructions for Form 8915-E say that you must file Form 8915-E if you received a coronavirus-related distribution.  If you report just an Other reason exception on Form 5329, it's likely to be questioned by the IRS.

I've revised by previous reply to suggest that filing just Form 5329 to claim an exception might be questioned by the IRS.