You don't amphib invade the city. You amphib one or two regions away. THEN march on the city with your whole army.
At least that's what I've seen. 
As for the idea of them splitting up and bringing in new players...that probably would work...the question is whether or not they WANT to do that...
If they don't want to, then it's their own fault for being invaded and I do not pity them
And you can always place militia on your seashore regions. Even if Thalmarking invades 2 regions beyond the city, their casulties will be rather high.
