Both options will be correct. if you file an extension and owe taxes, then you will need to pay the amount due by April 15 or a later date if filing and payment due date is extended again this year. An extension gives you more time to prepare your return, but it does not give you more time to pay.
If you file an extension, you can mark that you will pay on the due date. Then you will not have to worry about filing until October, but you will need to pay any amount due.
If you have a return coming, then you can just file an extension, or you can file your return and then amend after your hearing when everything is resolved.
You generally must file an amended return within three years of the date you filed the original return or within two years after the date you paid the tax, whichever is later.