Just get another provider while you still have your Verizon account open..

if you have paid for this month, you have the rest of this month to find another provider and have the number transferred.

Once you no longer have any account that is holding onto that phone number the number is open and I'm not sure how/if you can request a specific number.

Or wait till later in the month, or the end of the month.  You may be out some of the service you paid for but you will have a provider that is better for you.