What kind of firewall and switches are you running?
One option: if you're switches have stacking, then you can put them in a single stack and then create a port group that spans the two switches and then connect that to your NIC teams on the other end. This guards against switch failure, switchport failure, server NIC port failure, Ethernet cable failure, etc..
This adds a level of complexity that you don't have to deal with when using a simple team. But the plus side is higher bandwidth per connected server.
The "switch independant team" what bonding mode is that in linux? Is it mode 1, active/backup policy?
You will have to look at your individual network card's drivers and management software with regards to Linux. AKA, read the manual. My guess is that you're running Broadcom NICs and the management software that I've seen/used is called "Broadcom Advanced Control Suite 4" and the "switch independent mode" or team type is called, "Smart Load Balancing and Failover (SLB)".
I'm all Intel on the NIC side in this case as Supermicro is predominately intel NICs and they are very well supported both in freebsd and linux.
Contrary to Windows, linux actually have bonding of different types in the kernel (a module called bonding). So the drivers don't have to do bonding.
oh nice. I have no idea. I haven't done much with Linux lately. Still, I would read the NIC documentation as it pertains to Linux.