You could save those gift cards until you have enough and then you could pay off the purchase balance.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.
Yes I had the same problem it upset me a little for them to turn down money, you gotta pay it off in full ...
You could always purchase your phone from another place which allows you to make additional payments. No one is forcing you to purchase from Verizon.