I can successfully ssh from the same source machine in the remote 10.1.1.0/24 subnet to other devices in 192.168.0.0/24 subnet - just not the 2862 router itself.

I am still convinced it's something in the 2862 config/management firewall rules that is preventing ssh session from establishing.

changing port would be a good diagnostic step. Can you SSH to the router directly connected to it? Are there any firewall rules blocking port 22?