Can I use my permit number instead of a nonprofit authorization number?
No. A permit number and a nonprofit authorization number are completely different from the USPS perspective. A permit number is specific to the post office where it was created and is only relevant to that post office. It's your mailing "account" with that post office. A nonprofit authorization number is a unique number assigned to your nonprofit and recognized with the USPS, nationwide. It can be used with any permit, even one that belongs to your mail house. It lets the post office where your mail is being entered know that your organization is allowed to mail at the lower non-profit rates.