I would just keep your existing account active and set up call forwarding on the Verizon line so everyone can still contact you for the week.

You could either set up a T-Mobile account, or do the seven day test drive. They'll send you a phone with the latter option IIRC, so you don't have to unbox your new one. People you call will notice your number is different, but you can easily explain that you're trying a new line, and that the number is not permanent.

You can port the number to T-Mobile if you like the coverage, and if you don't, there's no harm done -- cancel call forwarding and continue your search. Be aware if you set up a new T-Mo account and you want the free international data you'll need to do the hard pull on your credit.