After plugging in the new lines into each device, and setting up their IPs, create a static route to the new IP of the other device and use the gateway of the new line for that route. repeat in the opposite direction then setup the tunnel using the new IPs.
You do not create a default route using the new ip, only a route to the other vpn line.
example:
1811 existing IP 1.1.1.1
1811 second (new) IP 2.2.2.2 - gateway 2.2.2.1
ASA existing IP 3.3.3.3
ASA new IP 4.4.4.4 - gateway 4.4.4.1 - nameif outside2
On 1811:
ip route 4.4.4.4 255.255.255.255 2.2.2.1
On ASA:
route outside2 2.2.2.2 255.255.255.255 4.4.4.1