That's not just it. You would pay $350 to cancel a line of service which is under contract just as anyone who cancels a line before completing a contract.
The fact you would then be opening a new line of service is up to you.
Additionally, you wouldn't have to go on DPP and make monthly payments by purchasing a new phone. You already have the phone you could activate on that new line of service, the one you purchased on contract. What did you plan to do with that phone. Just let is sit in a drawer and purchase a new phone? That seems kiind of silly. No, you would instead activate it on your new line of service and therefore have no monthly payments as you are not purchasing a new phone.
Whether or not you get your old number from the contract line you cancelled is another question altogether and I am not certain you would actually be able to do so, regardless what you have been told over the phone.
One thing to keep in mind when doing this would be to open the new line of service BEFORE you cancel the contract liine. In the customer agreement, if you cancel a line of service which is under contract and then open up a new line of service within 90 days, Verizon has in the past simply reinstated the contract which was in effect when you cancelled service, although I do not currently see that in the customer agreement. It is possible they do not do this anymore, but I can't say one way or the other as I have not done this previously.