Unfortunately teaming was not designed for the application you are describing. It was used so a large number of machine could access a central server and the server interfaces were being exceeded.
Even if you were to team 4 or 8 ports on your server and nas it would still only use 1. This is a fundamental thing on port aggregation works and the methods it uses to choose the port. There are some proprietary things where you can hook the nas and server directly but both have to support these non standard methods of combining nic cards. The vast majority only support the standard 802.3ad
This issue is part of the reason most enterprise installation have abandoned teaming and have gone to 10g ports.