In your configuration you have VBR --> ProxyVM --> ESXi
All backup/replica activity is performed against .vmdks and involves OS freezes, snapshot operations etc. All this magic is managed by ESXi host, which means that NBD commands issued by backup software have to be handled by VMkernel TCP/IP stack, which is strictly tied to your 1Gb NIC...
Considering all of the above, you have only three options:
1) upgrade your management NIC
2) use hot-add mode
3) get another management network on your vDS
Personally I'd stick to hot-add, because if you use NBD you will get an extra network overhead right between your proxy and ESXi.
I agree that hot-adding may take some time, but I'm curious how big is the difference between these modes in your case? Have you already compared the overall backup time for both?