Ok , so you need a review of your infrastructure. 
Because for lan backup, all software will use the same network that the management traffic. So in your case you will use a 1GB Link.
3 possibility Here :
- 1 : Buy an other 10 Gb network card and add it to the vswitch 0 , but expensive.
- 2 : Merge your vSwitch, and use explicit failover for use 10GB for your management traffic and 1GB in case of failure. (Create 3 port Group , 1 Management, 1 VM, and 1 vMotion)
For Exemple of explicit failover : I supposed vmnic 0 + 1 = 1GB and vmic 2+3 10GB.
- Port Group Management : Active vmnic 2 / Standby vmnic 3 / Unused vmnic1+0
- Port Group VM : Active vmnic1 + 0 / Standby / Unused vmnic 2+3
- Port Group vMotion : Active vmnic3 / Standby vmnic 2 / Unused vmnic1+0
- 3 : You can move a 1GB to your vswitch1 and a 10GB link to your vswitch0 and use explicit failover.
For Exemple of explicit failover : I supposed vmnic 0 + 1 = 1GB and vmic 2+3 10GB.
- Port Group Management : Active vmnic 2 / Standby vmnic 0
- Port Group VM : Active vmnic 1 + 0
- Port Group vMotion : Active vmnic 3 / Standby vmnic 1
Julien.