Router starts rebooting when I enable teaming on RN516

Does the NAS have a fixed IP address?
You could try disabling GRO in the router - apparently in LAN/ switch control part of router admin, although I believe asus may have removed/ disabled it because of the problems it caused. Check anyway.
Is the anything in the router logs that might give you a clue?
Have you asked the router manufacturer's support, this sounds like a router problem, not a readynas problem?

If there is a setting for GRO you should certainly start by disabling it.

Why not use standard IEEE standard LACP/LAG? - your switch supports it. That would almost certainly work around the problem since it is strictly layer-2, and would give you all the teaming benefits of ALB. I believe the GS116E has a web interface to configure this (my GS724T does), there is also a configuration utility you can download from netgear.com.

If for some reason you are determined to use ALB, if you are using dhcp (normally or with address reservation) for the NAS you might try switching to a static address. ALB messes with ARP, and that conceivably could be confusing the asus dhcp (esp. if you are using address reservation).

Thanks for the ideas guys!

GS108Tv2 is better for teaming than GS116E (no support for team that requires config on the switch side on that one...).

No logs on the router that helps either. I'll check if more detailed logging can be turned on.

Did have time in the last two weeks to play around. Without teaming everything runs fine, but it would be nice to be able to turn on.

You're right - I saw LAG supported in the configuration utility, and assumed that all the smartswitches supported it. However many of them don't (including the GS116E).

If you need to stick with the GS116E, then perhaps transmit load balancing is the best you can do. I suspect that will not create any issues with the router. If you can upgrade to a GS116T-200 switch, then you'd get LAG/LACP support.

Though teaming generally doesn't make that much difference in a home environment. Each session remains limited to 1 gbit, so it only helps when multiple users are accessing the NAS simultaneously for large sequential file transfers. If the files are small (or the users are doing random I/O), then you are usually limited by the disk seek performance, not the network.