How to retain an unlimited data line on Verizon, and get the upgrade discount (family plan needed)

Situation:

Family plan: Line A and B are both eligible for an upgrade discount. Line A has unlimited data. Line B has limited data.

What to do (online): Upgrade Line B using the upgrade discount. Then, transfer the upgrade on Line A to Line B. Upgrade line B again using the transferred upgrade discount. Receive both phones in mail. Call Verizon, and switch one of the phones to Line A.

Result: iPhone 5 with Unlimited Data and Verizon's wonderful 4G network.

I have spoke with many Verizon representatives to confirm that this will work.