A couple of questions...are you sure that isn't a Linksys Router instead of a Syslink Switch? I've never heard of the latter and I don't see any public IP address in your configs so you must have a router somewhere.
Second, I'm not really sure about your last statement. I'm assuming you just want to give the computers on the 10.0.0.0 network Internet access and do NOT want them to be able to route data to the workgroup LAN. Is that correct?
Assuming I'm right about these two things, I think you may be asking too much from Internet Connection Sharing, although I've never really tried a setup like this. Everything I've seen done with ICS assumes all the machines are on one happy little workgroup or at least network, together. My suggestion to save a lot of grief would be to get a second Linksys router. Plug it's WAN port into one of the switch ports of the first router and let it get it's wan IP automatically. Then plug your home network PCs into it. Don't bother with the 10.0.0.0 network stuff, just change the LAN config in the second router to use 192.168.1.1 for it's LAN IP and turn DHCP on. Set all the PCs to get their addresses automatically. It's really simple and everybody will be happy.