The best methods are indeed to either use Backup Assistant to restore the contacts, or to visit a Verizon store and have them use their equipment to transfer the data. Does the phone power up? If it is completely smashed and won't turn on, then there's probably not any way to get those contacts back unless you have them saved elsewhere.
If it does turn on, go through the steps on the new phone to install and activate Backup Assistant, and then mirror your actions exactly on the old phone. You can use the working screen on the new phone as your "eyes" since it should be identical on both devices. If that doesn't work, your options are pretty limited.
You might look into some software called BitPim. I don't know if it is compatible with the Convoy, but it facilitates a connection between your computer and phone, and allows you to download data like contacts. Then you could reverse the process with the new phone.